LESSON Representing Proportional Relationships 3-1 ...

Name ________________________________________ Date __________________ Class __________________

LESSON Representing Proportional Relationships

3-1

Practice and Problem Solving: A/B

Use the table to complete Exercises 1?3.

Feet 1

3 4

6

Inches

24

60

1. The table shows the relationship between lengths in feet and lengths in inches. Complete the table.

2.

Write each pair as a ratio.

inches feet

= 24 =

=

1

3

= 4

60

=

6

Each ratio is equal to _________________.

3. Let x represent feet. Let y represent inches.

An equation that describes the relationship is ___________________________.

Use the table to complete Exercises 4 and 5. Tell whether each relationship is proportional. If it is proportional, write an equation that describes the relationship. First define your variables.

Lemonade Recipe

Lemons 1

2

3

4

5

6

Sugar (c) 1.5 3 4.5 6 7.5 9

Water (c) 7 14 21 28 35 42

4. the ratio of lemons to cups of sugar

_________________________________________________________________________________________

5. the ratio of cups of sugar to cups of water

_________________________________________________________________________________________

Use the table to complete Exercise 6.

Distance Traveled Daily on a Family Road Trip

Hours

6

4.5

9

Distance (mi) 270 229.5 495

2

3.25 5.75

60 188.5 281.75

6. Is the relationship shown in the table below proportional? If so, what is the ratio of the hours driven to miles traveled?

_________________________________________________________________________________________

Original content Copyright ? by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

45

UNIT 2: Proportional and Nonproportional Relationships and Functions

MODULE 3 Proportional Relationships

LESSON 3-1

Practice and Problem Solving: A/B

1.

Feet

1

2

3

4

5

6

Inches

12 24 36 48 60 72

2. 12;

2;

36;

48;

5; 72;

12 1

or

12

3. y

=

12x, or

x=

12 y

or, x =

1 12

y

4. yes; let x = lemons and y = sugar;

y = 1.5x or let x = sugar and y = lemons;

y=

x 1.5

5. yes; let x = sugar and y = water;

y

=

4

2 3

x

or

y

4.7x,

or

let

x

=

water

and y = sugar; y = 3 x or y x

14

4.7

6. not a proportional relationship

Practice and Problem Solving: C

1. a. yes b. y = 1.9x

2. about 6.6 ft 3 a. yes

b. y = 50x c. 456.25 mi d. 11

Practice and Problem Solving: D

1. Yards 1 2 3 4 5 6

Feet 3 6 9 12 15 18

2. 2, 9, 4, 15 , 3 5

3. y = 3x

4. y = 50x

5. yes 6. yes 7. yes

Reteach

1.

Distance Driven (mi)

100 200 300 400 500 600

Gas Used (gal) 5 10 15 20 25 30

2. a. 10; 300; 20; 500 25

b. 20

3 a. number of miles driven b. y = 20x

Reading Strategies 1. y = 0.25x 2. $87.50 3.

Planet

Mercury Venus Earth Mars Jupiter

Diameter (mi)

3,032 7,521 7,926 4,222 88,846

Distance from Sun (millions of mi)

36.0

67.2 93.0 141.6 483.6

Ratio

84.2 111.9 85.2 29.8 183.7

4. No; The ratio between each pair of numbers is not the same.

Success for English Learners

1. 31 mi

2. Real-world distance is greater: 1 mile is greater than 1 inch.

LESSON 3-2

Practice and Problem Solving: A/B 1. -2 2. 4

3 3. $6.49 4. 65 mi/h

Original content Copyright ? by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

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