6 mskills. Read through each question, and check each response. y = 50x. y = 50x 25. y = 1. y = 50x + 25

(1)

2 1

3 2 1

Time (wk) 125

100

25 75 50 150

Cost ($)

O

Amy Joe y

x

75 60 45 30 15 90

Cost ($)

x Mimi

Zoe y

Zoe and Mimi each charge their customers $15 per hour to rent bikes.

Mimi also collects a $30 flat fee from each customer. Which equation can be used to express the amount Mimi charges to rent a bike for x hours?

Joey’s cleaning service charges $50 per week to clean a home. Amy’s cleaning service charges $50 per week, plus $25 for cleaning supplies. Which equation can be used to express the amount that Amy’s cleaning service charges?

y = 50x

y = 50x − 25

y = ___ 50 ¹ x

y = 50x + 25

y = 15x

y = 15x + 30

y = 30x

y = 30x + 15

✓

(2)

4

Time (h) x

Amount Charged ($) y

Amal Ji

175 2

75

100 225

3 150

0 0

1 125 50

Time (h) t

Earnings ($) e

Ben Kara

125 2

75

50 150

3 75

0 0

1 100 25

Ben and Kara both work in retail sales, earning the same hourly rate.

Ben recieves a one-time bonus. Which equations can be used to express both Ben’s and Kara’s earnings?

the amounts Amal and Ji charge per hour to rent their food trucks.

Which statement is true?

Ji charges $75 per hour.

Amal charges $75 per hour.

An equation that models Amal’s fee is y = 50x + 75.

Amal always charges $50 more than Ji.

Ben: e = 75t Kara: e = 25t

Ben: e = 75t + 25 Kara: e = 25t

Ben: e = 25t + 75 Kara: e = 25t

Ben: e = 25t + 75 Kara: e = 75t

✓

(3)

6

A streaming video plan costs $40 to set up and $25 per month.

Let c represent the total cost, in dollars, of using the plan for m months.

Select from the numbers and letters in the boxes to model the cost of the streaming video plan.

Let c represent the total cost, and m represent the number of months.

Select from the numbers and letters in the boxes to model the total cost of the gym membership.

c

m

25

¹

___ 40

50

25

75

40

= ⋅ + = ⋅ +

c c

25 50

m m

40

75

(4)

8

1

Time (h)

2 3 4

7

Cost ($)

42

35

28

21

14

O

x y

C (3, 35)

A (1, 21) B (2, 28)

1 2 3 4 5 6

180 210

150

120

90

60

30

O

x y

B (4, 210)

A (2, 120)

What is the slope of the line shown?

He charges an initial fee, plus an amount per hour.

How much does Davon charge per hour for a skateboard rental?

Davon charges $ per hour for a skateboard rental.

The slope of the line is ____ .

7 Answers will vary.

90

2

(5)

10

1 2 3 4 5 6 7 8 9

12 14

10 8 6 4 2 O

x y

B (4, 6) A (2, 4)

C (8, 10)

1 2 3 4 5 6 7 8 9

30 35

25 20 15 10 5

O

x y

A (4, 15)

B (8, 20)

Which is the equation of the line shown?

The slope of the line is equal to __ 2 ¹ .

The slope of the line is constant.

The line’s slope between points A and B is equal to the line’s slope between points B and C.

The line’s slope between points A and B is less than the line’s slope between points B and C.

y = __ 4 ¹ x + 10

y = __ ⁵4 x + 10

y = x + 10

y = 10x + __ ⁵ 4

✓

(6)

12

2 4 6 8 10 12 14 16 18 36

42 48 54 60 66 72

30 24 18 12 6 O

x y

A (4, 36)

B (10, 54)

5 ft

3 ft

?

9 ft

x

3 y

6

¹

__ 3

24

Tai designed a staircase with a height-to-base ratio of 3∶5.

The height of the staircase is 9 feet.

What should the base of Tai’s staircase measure?

the equation of the line shown.

= ⋅ +

24

The base of Tai’s staircase should measure feet.

y 3 x

15

(7)

14

y

24 30 36 18

12 6

Base (ft) 2

1 3 4

Height (ft)

O

x 6 ft

2 ft

3 ft 6 ft

8 ft 4 ft

12 ft 4 ft

Cassie is designing a wheelchair ramp for a school. Her original design had a height of 3 feet and a base of 24 feet. Her new design must have a height of 3 feet and a height-to-base ratio of 1∶12.

How long will the base of the ramp be in the new design?

a 1∶3 height-to-base ratio. Which of the following triangles have a 1∶3 height-to-base ratio?

6 feet

12 feet

30 feet

36 feet

✓

(8)

16

3 4 5 6

2 1

Time (yr) 2100

1800 1500

300 1200 900 600 2400

Cost ($)

O y

x

3 4 5 6

2 1

Distance (mi) 9

6 3 12

Cost ($)

O y

x

A taxi charges a $3 initial fee, plus $1.50 per mile traveled.

What is the total cost of a 4.5-mile taxi trip?

and $150 for annual maintenance. What are the total fees for building a new website and maintaining it for 3 years?

$1050

$1250

$1300

$1350

$9.00

$9.50

$9.75

$10.00

✓

(9)

18

x y

20

10 30 40 50 60 70

Weight (lb) 160

240

80 120 200

40 280

Cost ($)

O

3 4 5

2 1

Time (wk) 200

160 120 80 40

Cost ($)

O y

x

A dog walking service charges a $19 one-time fee, plus $40 per week.

The equation y = 40x + 19 models the cost of using the service.

y is the total cost in dollars, and x is the number of weeks. Kevin estimated the cost of using the service for 4 weeks to be about $180.

Which statement is true?

He also pays $50 for the lettuce to be delivered to his restaurant.

Select from the numbers in the boxes to estimate how many pounds of lettuce Steve can purchase and have delivered for $220.

10

60

30

80

50

90

Steve can purchase about pounds of organic lettuce and have it delivered to his restaurant for $220.

Kevin’s estimate is incorrect. When x = 4, the value of y is $116, which is not close to $180.

Kevin’s estimate is incorrect. When y = 4, the value of x is $116, which is not close to $180.

Kevin’s estimate is correct. When x = 4, the value of y is $179, which is close to $180.

Kevin’s estimate is correct. When y = 4, the value of y is $179, which is close to $180.

60 ✓

(10)

20

In the equation y = 5x + 12, what is the value of x if y = 62?

a delivery fee of $8 per order. The amount, y, that Andre charges for an order of x T-shirts is represented by the equation y = 19x + 8.

A customer paid $217 for an order of T-shirts.

How many T-shirts did the customer order?

8 T-shirts 11 T-shirts

18 T-shirts 25 T-shirts

The value of x is .

✓

10

(11)

plus $5 per month for unlimited access to streaming videos.

Part A: Write an equation with two variables to model the situation.

Define your variables. Explain your reasoning.

Part B: How much does a customer pay for 1 year of membership on FunFlix? Explain your reasoning.

Sample Answer:

Part A:

I let x represent the number of months of membership.

I let y represent the the total cost of membership per customer.

Since the membership costs $5 per month, plus the one-time fee of

$14, the equation that models this situation is y = 5x + 14.

Part B:

One year is 12 months, so I substituted 12 for the variable x, which represents the number of months, to find the total cost for a customer for 1 year of membership.

y = 5x + 14 y = 5(12) + 14

I multiplied 5 by 12 first to get y = 60 + 14. The total cost for a

membership for a year is $60 + $14, or $74.

(12)

3 4 5 6 2

1

Time (h) 50

40 30 20 10 60

Cost ($)

O y

x

membership fee, plus an hourly fee.

The graph shows the cost of using the gym.

Part A: What is the initial fee charged to customers for using the gym? What is the hourly rate? Explain your reasoning.

Part B: Lina has the option of purchasing an unlimited weekly pass at the gym for

$100. She normally uses the gym 3 times per week, no more than 2 hours each time. Is it cheaper for Lina to purchase the unlimited weekly pass?

Why or why not? Explain your reasoning.

Sample Answer:

Part A:

I found the initial fee from the y-axis on the graph. The line started at $20 on the y-axis, which means that a customer’s initial membership fee is $20.

The hourly rate is the slope of the line on the graph. Each hour, the line increases by $5, so the customer pays $5 per hour they use the gym.

Part B:

I found how many hours Lina uses the gym per week by multiplying 3 times per week by 2 hours each time, which is 6 total hours a week. So, for one week, Lina would pay the initial membership fee of $20 and then $5 for each hour she used the gym. Looking at the graph, 6 hours a week would cost Lina $50. Since

6 mskills. Read through each question, and check each response. y = 50x. y = 50x 25. y = 1. y = 50x + 25

✓

✓

✓

✓

c

c

m

m

25

50

25

75

40

c c

25 50

m m

40

75

7

Answers will vary.

90

2

✓

✓

✓

x

3

y

6

24

24

y 3 x

15

✓

✓

✓

✓

✓

10

60

30

80

50

90

60

✓

✓

10

Sample Answer:

Part A:

I let x represent the number of months of membership.

I let y represent the the total cost of membership per customer.

Since the membership costs $5 per month, plus the one-time fee of

$14, the equation that models this situation is y = 5x + 14.

Part B:

One year is 12 months, so I substituted 12 for the variable x, which represents the number of months, to find the total cost for a customer for 1 year of membership.

y = 5x + 14 y = 5(12) + 14

I multiplied 5 by 12 first to get y = 60 + 14. The total cost for a

membership for a year is $60 + $14, or $74.

Sample Answer:

Part A:

I found the initial fee from the y-axis on the graph. The line started at $20 on the y-axis, which means that a customer’s initial membership fee is $20.

The hourly rate is the slope of the line on the graph. Each hour, the line increases by $5, so the customer pays $5 per hour they use the gym.

Part B:

$100 > $50, it is not cheaper for Lina to purchase the unlimited weekly pass.