7th Grade Math

406 Linear Functions

Direct Variation

Words A direct variation is a

relationship in which

the ratio of y to x is a

constant, k. We say y

varies directly with x.

Model

y

O x

y = 3 x

Symbols

y

_

x

= k or y = kx,

where k ≠ 0

Example y = 3 x

In a direct variation equation, the constant rate of change, or slope, is

assigned a special variable, k.

As you have already learned, not all situations with a constant rate

of change are proportional relationships. Likewise, not all linear

functions are direct variations.

Determine Direct Variation

PIZZA Pizzas cost $8 each plus a $3 delivery charge. Make a table

and graph to show the cost of 1, 2, 3, and 4 pizzas. Is there a

constant rate? a direct variation?

Number

of Pizzas^1234

Cost ($) $11 $19 $27 $35

Pizza

16

8

0

24

12

4

20

28

32

36

40

123 4

(1, 11)

(2, 19)

(3, 27)

(4, 35)

Cost ($)

Number of Pizzas

__number of pizzascost _^11

1

, _^19

2

or 9.5, _^27

3

or 9, _^35

4

or 8.75

Because there is no constant rate, there is no direct variation.

b. FOOD COSTS Two pounds of cheese cost $8.40. Make a table and

graph to show the cost of 1, 2, 3, and 4 pounds of cheese. Is

there a constant rate? a direct variation?

Real-World Link

The average American

consumes 23 pounds

of pizza every year.

T

RRReal-World Link

404_415_C07_L3_895130.indd 406 12/31/09 4:32 PM