11.2
Direct and Inverse Variation
How are banking angle and turning radius related?
Goal
Use direct and inverse
variation.
In Lesson 4.6 you studied direct
variation. In Example 4 you will use
a different kind of variation to relate
the banking angle of a bicycle to its
turning radius.
Key Words
• direct variation
• inverse variation
• constant of variation
In this lesson you will review direct variation and learn about inverse variation,
where the product of two variables is a constant.
MODELS FOR DIRECT AND INVERSE VARIATION
Student Help
STUDY TIP
Direct and inverse
variation are
sometimes called
direct and inverse
proportions.
Direct Variation
y
y kx
k>0
The variables x and y vary directly if for a
constant k
y
k, or y kx, where k 0.
x
x
Inverse Variation
y
k
y x
k>0
The variables x and y vary inversely if for a
constant k
k
x
xy k, or y , where k 0
x
The number k is the constant of variation.
EXAMPLE
1
Use Direct Variation
Find an equation that relates x and y such that x and y vary directly, and y 4
when x 2.
Solution
Write the direct variation model.
y
k
Substitute 2 for x and 4 for y.
4
k
2
Simplify the left-hand side.
2k
ANSWER 䊳
y
x
The direct variation that relates x and y is 2, or y = 2x.
11.2
Direct and Inverse Variation
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