1. Ch. 11Vocabulary 5) Inverse variation
6.) constant of variation (for an inverse variation)

2. 11-6A Inverse Variation
Algebra 1

3. The variables x and y vary directly if, for a constant k,
USING DIRECT AND INVERSE VARIATION
DIRECT VARIATION
The variables x and y vary directly if, for a constant k, y x = k, or
y = kx,
k  0.

4. The variables x and y vary inversely, if for a constant k,
USING DIRECT AND INVERSE VARIATION
INDIRECT VARIATION
The variables x and y vary inversely, if for a constant k, k x = y, or
xy = k,
k  0.

5. MODELS FOR DIRECT AND INVERSE VARIATION
USING DIRECT AND INVERSE VARIATION
MODELS FOR DIRECT AND INVERSE VARIATION
DIRECT VARIATION
INVERSE VARIATION k x = y
y = kx
k > 0
k > 0

6. Example 1
When x is 3, y is 12. Find an equation that x and y vary inversely.

7. Example 2
Does the date in each table represent a direct variation or an inverse variation? For each, write an equation to model the data.
A.) B.) x Y 4
-12 6 -8 8 -6 x y 4
-12 6
-18 8
-24

8. An 8 sliced pizza is share equally by a group of friends.
Example 3 Tell whether each situation represents a direct variation or inverse variation. Explain your reasoning.
An 8 sliced pizza is share equally by a group of friends.

9. Assignment

10. Example 3
Decide if the data in the table show direct or inverse variation. Write an equation that relates the variables.
#37 on pg. 660

11. Compare the direct variation model and the inverse
Comparing Direct and Inverse Variation
Compare the direct variation model and the inverse
variation model you just found using x = 1, 2, 3, and 4.
SOLUTION
Plot the points and then connect the points with a smooth curve.
Direct Variation: the graph for this model is a line passing through the origin.
Direct
y = 2x
Inverse Variation: The graph for this model is a curve that gets closer and closer to the x-axis as x increases and closer and closer to the y-axis as x gets close to 0.
Inverse 8 x
y =

12. Example 2
Make a table of values for x = 1, 2, 3 and 4. Use the table to sketch a graph. Decide whether x and y vary directly or inversely.
#33 pg. 659

13. Compare the direct variation model and the inverse
Comparing Direct and Inverse Variation
Compare the direct variation model and the inverse
variation model you just found using x = 1, 2, 3, and 4.
Make a table using y = 2x and y = 8 x
SOLUTION 8 x
y =
y = 2x 1 2 3 4 6
Direct Variation: k > 0.
As x increases by 1,
y increases by 2.
Inverse Variation: k > 0.
As x doubles (from 1 to 2),
y is halved (from 8 to 4).