1. Tell whether the equation represents direct variation.
Example 1
Identifying Direct Variation from an Equation
Tell whether the equation represents direct variation. a. – 2x + y = b. – 2x + y = 3
SOLUTION
Solve each equation for y. y 2x = + – a. 2x y =
The equation can be written in the form where k 2, so it represents direct variation. = y kx

2. The equation cannot be written in the form ,
Example 1
Identifying Direct Variation from an Equation b. – 2x + y = 3 2x y = + 3
The equation cannot be written in the form ,
so it does not represent direct variation. = y kx 2

3. Tell whether the table represents direct variation.
Example 2
Identifying Direct Variation from a Table
Tell whether the table represents direct variation. a. x 1 2 3 4 5 y 6 10 14 18 22 b. y x 3 2 1 4 5 8 12 16 20
SOLUTION
For each table, determine whether the ratios of y to x are constant. 3

4. Because , the ratios are not constant. So,
Example 2
Identifying Direct Variation from a Table
Because , the ratios are not constant. So,
the table does not represent direct variation. = 1 6 2 10 a.
Because , the ratios are constant. So, the table represents direct variation. 3 12 1 4 2 8 = 16 5 20 b. 4

5. Graph the equation from part (a). What does the slope represent?
Example 3
Using Direct Variation
BUYING CDS
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.
a. Write a direct variation equation for the situation that relates x and y.
Graph the equation from part (a). What does the
slope represent?
c. Find the cost to buy 7 of the CDs on sale.

6. Use the fact that y 36 when x 3 to write a direct variation equation.
Example 3
Using Direct Variation
SOLUTION a.
Use the fact that y when x 3 to write a direct variation equation. = = 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. = 6

7. Make a table of values for the equation y 12x. x 1 2 3 4 5 y 12 24 36
Example 3
Using Direct Variation b.
Make a table of values for the equation y 12x. x 1 2 3 4 5 y 12 24 36 48 60 =
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. 7

8. Example 3
Using Direct Variation c.
To find the cost of 7 CDs, substitute 7 for x in the equation from part (a). y =
12x
Write direct variation equation.
Substitute 7 for x. = 12 ( ) 7 = 84
Simplify.
ANSWER
The cost to buy 7 CDs is $84. 8

9. Tell whether the equation or table represents direct variation.
Guided Practice
for Examples 1, 2, and 3
Tell whether the equation or table represents direct variation. 1. 3x y =
ANSWER
yes 2. y x = + –
ANSWER
yes 3. 1 y x = + 3
ANSWER no y x 3 2 1 4 6 9 12 4.
ANSWER
yes

10. Tell whether the equation or table represents direct variation.
Guided Practice
for Examples 1, 2, and 3
Tell whether the equation or table represents direct variation. y x 3 2 1 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