Example 1 Identifying Direct Variation from an Equation

Tell whether the equation represents direct variation.

SOLUTION

Solve each equation for y.

a. 0y2x =+–

2xy =

b. 3y2x =+–

0y2x =+–a.

The equation can be written in the form where k 2, so it represents direct variation.

==

y kx

Example 1

b. 3y2x =+–

2xy = + 3

Identifying Direct Variation from an Equation

The equation cannot be written in the form , so it does not represent direct variation.

=y kx

Example 2

Tell whether the table represents direct variation.

SOLUTION

For each table, determine whether the ratios of y to x are constant.

a.

yx 321 4 5

6 10 14 18 22

Identifying Direct Variation from a Table

b.

yx 321 4 5

4 8 12 16 20

Example 2 Identifying Direct Variation from a Table

Because , the ratios are

constant. So, the table represents direct variation.3

1214

28

= =4

16=

520

=b.

Because , the ratios are not constant. So,

the table does not represent direct variation.

=16

210a.

Example 3

At a music store sale, the amount y (in dollars) that you spend varies directly with the number x of CDs that you buy at the sale price. You pay $36 for 3 of the CDs on sale.

BUYING CDS

Using Direct Variation

a. Write a direct variation equation for the situation that relates x and y.

b. Graph the equation from part (a). What does the slope represent?

c. Find the cost to buy 7 of the CDs on sale.

Example 3 Using Direct Variation

y = kx Write direct variation equation.

Substitute 36 for y and 3 for x.36 = k ( )3

12 = k Solve for k.

ANSWER

A direct variation equation that relates x and y is y 12x.=

SOLUTION

Use the fact that y 36 when x 3 to write a direct variation equation.

= =a.

b.

Example 3 Using Direct Variation

=

Make a table of values for the equation y 12x.

yx 210 3 4

0 12 24 36 48560

Plot the points from the table, and draw a line through the points. The slope of the line is 12 and represents the cost (in dollars) per CD.

c.

Example 3 Using Direct Variation

y = 12x Write direct variation equation.

Substitute 7 for x.= 12( )7

= 84 Simplify.

ANSWER The cost to buy 7 CDs is $84.

To find the cost of 7 CDs, substitute 7 for x in the equation from part (a).

ANSWER yes

Guided Practice for Examples 1, 2, and 3

Tell whether the equation or table represents direct variation.

1. 3xy =

2. 0yx =+– ANSWER yes

3. 1yx =+3 ANSWER no

yx 321 4

3 6 9 12

4. ANSWER yes

Guided Practice for Examples 1, 2, and 3

Tell whether the equation or table represents direct variation.

yx 321 4

8 9 10 11

5.

ANSWER no

6. WHAT IF? In Example 3, suppose you want to buy 9 of the CDs that are on sale. How much will this cost?

ANSWER $108