Ch. 11Vocabulary
• 5) Inverse variation
• 6.) constant of variation (for an inverse
variation)
11-6A Inverse Variation
Algebra 1
USING DIRECT AND INVERSE VARIATION
DIRECT VARIATION
The variables x and y vary directly if, for a constant k,
y
= k,
x
or
y = kx,
k  0.
USING DIRECT AND INVERSE VARIATION
INDIRECT VARIATION
The variables x and y vary inversely, if for a constant k,
k
= y,
x
or
xy = k,
k  0.
USING DIRECT AND INVERSE VARIATION
MODELS FOR DIRECT AND INVERSE VARIATION
DIRECT VARIATION
y = kx
k>0
INVERSE VARIATION
y =
k>0
k
x
Example 1
• When x is 3, y is 12. Find an equation that x
and y vary inversely.
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
x
Y
4
-12
4
-12
6
-18
6
-8
8
-24
8
-6
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.
Assignment
Example 3
• Decide if the data in the table show direct or
inverse variation. Write an equation that
relates the variables.
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.
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.
Direct
y = 2x
Inverse
y= 8
x
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.
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
Make a table using y = 2x and y = x8 .
x
1
2
3
4
Direct Variation: k > 0.
As x increases by 1,
y increases by 2.
y = 2x
2
4
6
8
Inverse Variation: k > 0.
As x doubles (from 1 to 2),
y is halved (from 8 to 4).
y = x8
8
4
8
3
2