?

Total Cost for Video Game Rental

Number of games rented

Cost

($)

5

O

10

15

20

6 82

y

x

4

ESSENTIAL QUESTION

EXPLORE ACTIVITY

Graphing Linear RelationshipsTeresa signs up for a membership to rent video games. The company charges $5 per month and $2 per video game. Graph a linear relationship between the number of games Teresa rents and her monthly cost.

Make a table. Record different values for the linear relationship.

Number of video games rented Monthly cost ($)

0 5 + 2(0) = 5

1 5 + 2(1) =

2 5 + 2( ) =

3 5 + 2( ) =

4 5 + 2( ) =

Use the table to create ordered pairs:

(0, 5), (1, 7), (2, 9), (3, 11), (4, 13)

Reflect1. Do the values between the points make sense in this context? Explain.

STEP 1

STEP 2

How do you write and graph a linear relationship?

L E S S O N

7.2Writing and Graphing Equations in the Form y = mx + b

7.7

Expressions, equations, and relationships—7.7 The student is expected to represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b.

Plot each ordered pair on

the coordinate grid.

To find the monthly cost,

multiply the number of

video games rented by 2

and then add 5.

233Lesson 7.2

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

• Im

age

Cred

its: ©

Asia

Imag

es G

roup

/Get

ty Im

ages

Math On the Spotmy.hrw.com

Math TrainerOnline Assessment

and Intervention

Personal

my.hrw.com

Write an equation to describe the linear relationship.

2. The temperature of a pot of water is 45 °F. The temperature increases by 20 °F per minute when being heated.

3. A bamboo reed is planted when it is 12 centimeters tall. It grows 2.2 centimeters per week.

YOUR TURN

Writing Linear RelationshipsYou can write an equation to describe a linear relationship. The equation of a linear relationship is y = mx + b, where m is the rate of change and b is the value of y when x is 0.

Anthony runs a bicycle courier company that charges $3 per delivery plus $0.50 per mile. Write an equation to describe the linear relationship.

Make a table. Record different values for the linear relationship.

Distance (miles) Cost ($)

0 3 + 0.5(0) = 3

1 3 + 0.5(1) = 3.5

2 3 + 0.5(2) = 4

3 3 + 0.5(3) = 4.5

4 3 + 0.5(4) = 5

Write an equation for the delivery cost y for x miles traveled.

When distance is 0, the cost is $3. With each additional mile, the cost increases by $0.50.

Cost = $0.50 times number of miles plus $3 charge

y = 0.5 • x + 3

The equation is y = 0.5x + 3.

EXAMPLE 1

STEP 1

STEP 2

Math TalkMathematical Processes

7.7

Would all values between the given distances make

sense? Explain.

Unit 4234

© Houghton Miff

lin Harcourt Pub

lishing

Com

pany

Math On the Spot

my.hrw.com

Charlie’s Savings

Number of weeks

Am

ount

($)

80

O

160

240

320

400

480

y

x

2 4 6 8 10

Representing Linear Relationships Using Multiple RepresentationsThere are several ways to represent a linear relationship.

Charlie starts with $350 in his savings account. He withdraws $15 per week from his account. Represent the relationship using a table, an equation, and a graph.

Make a table. Record different values for the linear relationship.

Write an equation for the amount of money y in the savings after x weeks.

$350 minus $15 times the number of weeks

y = 350 - 15x

Use the table to create ordered pairs and then plot the data.

Reflect4. Does it make sense to connect the points on the graph with a line?

Explain.

5. Does an ordered pair with a negative y-value make sense in the situation?

EXAMPLEXAMPLE 2

STEP 1

STEP 2

STEP 3

Animated Math

my.hrw.com

Week Amount ($)

0 350 - 15(0) = 350

1 350 - 15(1) = 335

2 350 - 15(2) = 320

3 350 - 15(3) = 305

4 350 - 15(4) = 290

7.7

235Lesson 7.2

© Houghton Miff

lin Harcourt Pub

lishing

Com

pany

Pool Water

Time (min)

Am

ount

of p

ool w

ater

(L)

10

O

20

30

40

50

y

x

5 10 15 20 25

Math TrainerOnline Assessment

and Intervention

Personal

my.hrw.com

Bike Rental

Time (h)

Cost

($)

20

O

40

60

80

y

x

2 4 6 8 10

6. A bicycle rental company charges $18 to rent a bicycle, plus $7 for every two hours of rental time. Represent the relationship using a table, an equation, and a graph.

Hours rented Cost ($)

0

2

4

6

8

Equation:

YOUR TURN

Graph the linear relationship. (Explore Activity)

1. A pool contains 5 liters of water, and 10 liters of water are being poured into the pool every 5 minutes.

Write an equation to describe the linear relationships. (Example 1)

2. A moving company charges a $50 flat fee and $55 per hour to move.

y = x +

3. Anne has $250 in a savings account. She withdraws $5 per month.

y = x +

4. Erin owns $375 worth of comic books. She spends $15 every week on new comic books. Represent the relationship using a table and an equation. (Example 2)

5. How can you use a table of data to write and graph a linear relationship?

ESSENTIAL QUESTION CHECK-IN?? y = x +

Guided Practice

Week Total Comics ($)

0 375 + 15(0) = 375

1 375 + 15 =

2 375 + 15 =

3 375 + =

4 375 + =

Unit 4236

© Houghton Miff

lin Harcourt Pub

lishing

Com

pany

Personal Math Trainer

Online Assessment and

Interventionmy.hrw.com

Cab Ride Charges

Distance traveled (mi)

Cost

($)

2

4

6

8

10

2 4 6 8 10

y

xO

Name Class Date

Independent Practice7.2

A cab company charges a $3.50 boarding fee and $0.50 per mile.

6. Write an equation to describe the relationship between the cost of the cab ride and the number of miles traveled.

7. Graph the linear relationship.

8. Draw Conclusions Does it make sense to draw a line through the points? Explain.

9. What If? Suppose that the boarding fee was changed to $5. How would the graph change?

For 10–13 write an equation to represent the given linear relationship. Then state the meaning of the given ordered pair.

10. A plain medium pizza costs $8.00. Additional toppings cost $0.85 each. (4, 11.4)

11. Luis joined a gym that charges a membership fee of $99.95 plus $7.95 per month. (9, 171.5)

12. A tank currently holds 35 liters of water, and water is pouring into the tank at 15 liters per minute. (5.5, 117.5)

13. Jonas is riding his bicycle at 18 kilometers per hour, and he has already ridden for 40 kilometers. (6, 148)

14. Analyze Relationships How can you use an equation of a linear relationship to verify the points on the graph of the relationship?

7.7

237Lesson 7.2

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Work Area

y

x

O

15. Multiple Representations A furniture salesperson earns $750 per week plus a 15% commission on all sales made during the week.

a. Complete the table of data.

Weekly Sales ($) Earnings ($)

0

1,000

2,000

3,000

4,000

b. Graph the values in the table.

c. Write a linear equation to describe the relationship.

16. Make a Conjecture Can you draw a straight line through the points? Explain.

17. Analyze Relationships What are the advantages of portraying a linear relationship as a table, graph, or equation?

18. Critical Thinking Describe when it would be more useful to represent a linear relationship with an equation than with a graph.

19. Communicate Mathematical Ideas How can you determine when to draw a line through the points on the graph of a linear relationship?

FOCUS ON HIGHER ORDER THINKING

Unit 4238

© Houghton Miff

lin Harcourt Pub

lishing

Com

pany