NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Practice 8.5(F)

SCORE ___________

Distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.

Multi-Step Example Which table does NOT show a proportional relationship? A

C

Number of Tickets

2

3

4

5

Cost ($)

4

6

8

10

Number of Tickets

2

3

4

5

Cost ($)

5

7

9

11

B

D

Number of Tickets

1

2

3

4

Cost ($)

3

6

9

12

Number of Tickets

1

2

3

4

Cost ($)

5

10

15

20

Table A: Each x-value is multiplied by 2 to get each y-value. So the equation y = 2x represents the data in the table. y = 2x is in the form y = kx, so the relationship is proportional. Table B: Each x-value is multiplied by 3 to get each y-value. So the equation y = 3x represents the data in the table. y = 3x is in the form y = kx, so the relationship is proportional. Table C: Each x-value is multiplied by 2 and then 1 is added to get each y-value. So the equation y = 2x + 1 represents the data in the table. y = 2x + 1 is NOT in the form y = kx, so the relationship is NOT proportional. Table D: Each x-value is multiplied by 5 to get each y-value. So the equation y = 5x represents the data in the table. y = 5x is in the form y = kx, so the relationship is proportional. So, Table C does NOT represent a proportional relationship. 1 What value of m makes the equation y + m = 6x + 15 a proportional relationship?

B y – 4 = 2x – 4 C y = –0.4x – 3 D y + 5 = 5x + 5 3 Which equation represents the relationship between the x- and y-values in the table? Number of Quarts

4

20

28

48

100

Number of Gallons

1

5

7

12

25

F y = 4x Gy= x 2 Which equation does NOT show a proportional relationship? A y – 2 = 0.5x – 2 Course 3 • Proportionality

Hy= x+4 Jy=

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NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Practice 8.5(F) (continued) 4 Which is a proportional relationship?

SCORE ___________ 5 Which table does NOT show a proportional relationship? F G

H J

Time (weeks)

3

2

1

0

Height (cm)

15

10

5

0

Time (weeks)

3

4

5

6

Height (cm)

12

16

20

24

Time (weeks)

8

6

5

4

Height (cm)

4

3

2.5

2

Time (weeks)

5

6

7

8

Height (cm)

27

32

37

42

6 Which shows a proportional relationship?

A

x

–2

–1

1

2

y

–2

–3

–4

–5

x

–2

–1

1

2

y

1

0.5

–0.5

–1

C

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Course 3 • Proportionality