Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage1
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage2
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage3
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage4
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage5
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage6
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage7
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage8
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage9
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage10
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage11
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage12
4-2 Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
10.
(3, 1), slope 2
ANSWER:
y
= 2x
−
5
11.
(
−
1, 4), slope
−
1
ANSWER:
y
=
−
x
+ 3
12.
(1, 0), slope 1
ANSWER:
y
= x
−
1
13.
(7, 1), slope 8
ANSWER:
y
= 8x
−
55
14.
(2, 5), slope
−
2
ANSWER:
y
=
−
2x + 9
15.
(2, 6), slope 2
ANSWER:
y
= 2x + 2
Write an equation of the line that passes through each pair of points.
16.
(9,
−
2), (4, 3)
ANSWER:
y
=
−
x
+ 7
17.
(
−
2, 5), (5,
−
2)
ANSWER:
y
=
−
x
+ 3
18.
(
−
5, 3), (0,
−
7)
ANSWER:
y
=
−
2x
−
7
19.
(3, 5), (2,
−
2)
ANSWER:
y
= 7x
−
16
20.
(
−
1,
−
3), (
−
2, 3)
ANSWER:
y
=
−
6x
−
9
21.
(
−
2,
−
4), (2, 4)
ANSWER:
y
= 2x
22.
CCSSMODELING
Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5
feet away. After 2 seconds the car is 35 feet away.
a.
Write a linear equation to find the distance d of the car from Greg.
b.
Estimate the distance the car has traveled after 10 seconds.
ANSWER:
a.
d
= 15t + 5
b.
155 ft
23.
ZOOS
In 2006, the attendance at the Columbus Zoo and Aquarium was about 1.6 million. In 2009, the zoo
’
s
attendancewasabout2.2million.
a.
Write a linear equation to find the attendance (in millions) y after x years. Let x be the number of years since
2000.
b.
Estimatethezoo’
s attendance in 2020.
ANSWER:
a. y = 0.2x + 0.4
b. 4.4 million
24.
BOOKS
In 1904, a dictionary cost 30
¢
. Since then the cost of a dictionary has risen an average of 6
¢
per year.
a.
Write a linear equation to find the cost C of a dictionary y years after 2004.
b.
If this trend continues, what will the cost of a dictionary be in 2020?
ANSWER:
a.
C
= 30 + 6y
b.
$7.26
Write an equation of the line that passes through the given point and has the given slope.
25.
(4, 2), slope
ANSWER:
26.
(3,
−
2), slope
ANSWER:
y
= x
−
3
27.
(6, 4), slope
ANSWER:
y
=
−
x + 8
28.
(2,
−
3), slope
ANSWER:
y
= x
−
4
29.
(2,
−
2), slope
ANSWER:
y
= x
−
2
30.
(
−
4,
−
2), slope
−
ANSWER:
y
=
−
x
−
4
31.
DOGS
In 2001, there were about 56.1 thousand golden retrievers registered in the United States. In 2002, the
number was 62.5 thousand.
a.
Write a linear equation to find the number of golden retrievers G that will be registered in year t, where t = 0 is
the year 2000.
b.
Graph the equation.
c.
Estimate the number of golden retrievers that will be registered in 2017.
ANSWER:
a.
G
= 6.4t + 49.7
b.
c.
158,500
32.
GYMMEMBERSHIPS
A local recreation center offers a yearly membership for $265. The center offers
aerobics classes for an additional $5 per class.
a.
Write an equation that represents the total cost of the membership.
b.
Carly spent $500 one year. How many aerobics classes did she take?
ANSWER:
a.
y
= 5x + 265
b.
47 classes
33.
SUBSCRIPTION
A magazine offers an online subscription that allows you to view up to 25 archived articles free.
To view 30 archived articles, you pay $49.15. To view 33 archived articles, you pay $57.40.
a.
What is the cost of each archived article for which you pay a fee?
b.
What is the cost of the magazine subscription?
ANSWER:
a.
$2.75
b.
$35.40
Write an equation of the line that passes through the given points.
34.
(5,
−
2), (7, 1)
ANSWER:
y
= 1 x
−
9
35.
(5,
−
3), (2, 5)
ANSWER:
36.
ANSWER:
y
= x
+
37.
ANSWER:
y
=
−
x
−
Determine whether the given point is on the line. Explain why or why not.
38.
(3,
−
1);
ANSWER:
No; substituting 3 and
−
1 for x and y respectively, results in an equation that is not true.
39.
(6,
−
2);
ANSWER:
Yes; substituting 6 and
−
2 for x and y respectively, results in and equation that is true.
Determine which equation best represents each situation. Explain the meaning of each variable.
40.
CONCERTS
Tickets to a concert cost $8 each plus a processing fee of $4 per order.
ANSWER:
C; x represents the number of tickets per order and y represents the total cost of an order.
41.
FUNDRAISING
The freshman class has $225. They sell raffle tickets at $2 each to raise money for a field trip.
ANSWER:
B; x represents the number of raffle tickets sold, y represents the total amount of money in the treasury.
42.
POOLS
The current water level of a swimming pool in Tucson, Arizona, is 6 feet. The rate of evaporation is
inchperday.
ANSWER:
A; x represents the number of days, y represents the total depth of water in inches of the pool.
43.
CCSS SENSE-
MAKING
A manufacturer implemented a program to reduce waste. In 1998 they sent 946 tons of
waste to landfills. Each year after that, they reduced their waste by an average 28.4 tons.
a.
How many tons were sent to the landfill in 2010?
b.
In what year will it become impossible for this trend to continue? Explain.
ANSWER:
a.
605.2
b.
2032; In that year the waste would be 0 tons. After that, the waste would be a negative amount, which is
impossible
.
44.
COMBINING FUNCTIONS
The parents of a college student open an account for her with a deposit of $5000,
and they set up automatic deposits of $100 to the account every week.
a.
Write a function d(t) to express the amount of money in the account t weeks after the initial deposit. d(t) = 5000 +
100t
b.
The student plans on spending $600 the first week and $250 in each of the following weeks for room and board
and other expenses. Write a function w(t) to express the amount of money taken out of the account each week.
c.
Find B(t) = d(t)
–
w(t). What does this new function represent?
d.
Will the student run out of money? If so, when?
ANSWER:
a.
d(t) = 5000 + 100t
b
. w(t) = 600 + 250t
c.
B(t) = 4400
–
150t ; the amount remaining in the account at time t
d.
yes; in about 29 weeks
45.
CONCERTTICKETS
Jackson
is ordering tickets for a concert online. There is a processing fee for each order,
and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.
a.
Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.
b.
Make a table of values for at least three other numbers of tickets.
c.
Graph this equation. Predict the cost of 8 tickets.
ANSWER:
a.
$15; C = 52t + 15
b.
c.
$431
Number of Tickets
3
4
6
7
Cost ($)
171
223
327
379
46.
MUSIC
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and
then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25.
a.
Determine the cost of each CD for a member.
b.
Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.
c.
Graph this equation.
ANSWER:
a.
$5.25
b.
y
= 5.25x + 22
c.
47.
ERRORANALYSIS
Tess and Jacinta are writing an equation of the line through (3,
−
2) and (6, 4). Is either of
them correct? Explain your reasoning.
ANSWER:
Jacinta; Tess switched the x- and y-coordinates on the point that she entered in step 3.
48.
CHALLENGE
Consider three points, (3, 7), (
−
6, 1) and (9, p ), on the same line. Find the value of p and explain
your steps.
ANSWER:
11; Use the first two points to find the equation of the line, then replace x and y with 9 and p , respectively, to solve
for p.
49.
REASONING
Consider the standard form of a linear equation, Ax + By = C.
a.
Rewrite equation in slope-intercept form.
b.
What is the slope?
c.
What is the y-intercept?
d.
Is this true for all real values of A, B, and C?
ANSWER:
a.
b.
c.
d.
No, B
≠0
50.
OPENENDED
Create a real-world situation that fits the graph shown. Define the two quantities and describe the
functional relationship between them. Write an equation to represent this relationship and describe what the slope
and y-intercept mean.
ANSWER:
Sample answer: Let y represent the number of quarts of water in a pitcher, and let x represent the time in seconds
that water is pouring from the pitcher. As time increases by 1 second, the amount of water in the pitcher decreases
by
qt.Anequationis
y =
−
x + 4. The slope is the rate at which the water is leaving the pitcher,
quartper
second. The y-intercept represents the amount of water in the pitcher when it is full, 4 qt.
51.
WRITINGINMATH
Linear equations are useful in predicting future events. Describe some factors in real-world
situations that might affect the reliability of the graph in making any predictions.
ANSWER:
Sample answer: If the problem is about something that could suddenly change, such as weather or prices, the graph
could suddenly spike up. You need a constant rate of change to produce a linear graph.
52.
CCSSARGUMENTS
What information is needed to write the equation of a line? Explain.
ANSWER:
You need to know the slope and y-intercept of the line, the slope and the coordinates of another point on the line, or
the coordinates of two points on the line.
53.
Which equation best represents the graph?
A
y
= 2x
B
y
=
−
2x
C
D
ANSWER:
D
54.
Roberto receives an employee discount of 12%. If he buys a $355 item at the store, what is his discount to the
nearest dollar?
F
$3
G
$4
H
$30
J
$43
ANSWER:
J
55.
GEOMETRY
The midpoints of the sides of the large square are joined to form a smaller square. What is the area
of the smaller square?
A
64 cm
2
B
128 cm
2
C
248 cm
2
D
256 cm
2
ANSWER:
B
56.
SHORTRESPONSE
If
,whatisthevalueof3
x
−
9?
ANSWER:
15
eSolutionsManual-PoweredbyCogneroPage13
4-2 Writing Equations in Slope-Intercept Form
