Algebra 4
Section 9-1: Inverse Variation
Learning Objective: To use inverse variation.
Standard: A2.5.A and A2.5.E
Common Core: F-BF and F-LE
A. Using Inverse Variation:
1. In Chapter 2 you learned about Direct Variation: As x increased, y also increased by
the same constant value (k). y = kx, where k = y/x.
2. Inverse Variation: As x increases, y will decrease by the same constant value (k). y =
k, where k = xy (k = constant of variation).
x
Rate │ Time │ k (rt)
3
│ 8 │3(8) = 24
6
│ 4 │6(4) = 24
12 │ 2 │12(2) = 24
24 │ 1 │24(1) = 24
Constant of Variation: k = 24
Inverse Function: y = 24/x
a. Suppose that x and y vary inversely, and x = 3 and y = -5, write a function that
models the variation. y = k/x, k = xy = 3(-5) = -15, so y = -15/x
3. Identifying Direct and Inverse Variations:
a. x │ 0.5 │ 2 │ 6 │
y │ 1.5 │ 6 │ 18│
y/x: 1.5/0.5 = 3, 6/2 = 3, 18/6 = 3
Direct Variation
b. x │ 0.2 │ 0.6 │ 1.2 │
y │ 12 │ 4 │ 2 │
xy: 0.2(12) = 2.4, 0.6(4) = 2.4, 1.2(2) = 2.4
Inverse Variation
c. x │ 1 │ 2 │ 3 │
y │ 2 │ 1 │ 0.5 │
xy: 1(2) = 2, 2(1) = 2, 3(0.5) = 1.5
y/x: 2/1 = 2, ½ = 0.5, 0.5/3 = 0.167
No Variation
4. Suppose that x and y vary inversely. If x = 4 when y = 2, find y when x = 8.
a. If x and y vary inversely, then the constants of variation (k) should equal each other:
4(2) = 8(y), y = 8/8 = 1