1. Inverse Variation
Chapter 8
Section 8.10

2. Objective
Students will use inverse variation to solve problems

3. Concept
The table shows the time t, that it takes a car to travel a distance of 40 mi at the speed of r mi/h. You can see that rt = 40. Notice that if the speed is increased, the time is decreased, so that the product is always 40. You can say that the time varies inversely as the rate.
Rate
Time 20 2 30
4/3 40 1 50
4/5

4. Concept
An inverse variation is a function defined by an equation of the form xy = k, where k is a nonzero constant, or y = k/x, where x ≠ 0 You say that y varies inversely as x or that y is inversely proportional to x. The constant k is the constant of variation

5. Concept
Let (x1, y1) and (x2, y2) be two ordered pairs of the same inverse variation. Since the coordinates must satisfy the equation xy = k, you know that x1y1 = k and x2y2 = k, or x1y1 = x2y2 You can compare the equations for direct variation and inverse variation

6. Concept
Direct Variation Inverse Variation y = kx xy = k, or y = k / x y1 / x1 = y2 / x2 x1y1 = x2y2

7. Concept
The equations show that for direct variation the quotients of the coordinates are constant and for inverse variation the products of the coordinates are constant

8. Find the missing value m1 = 24, d1 = 30, m2 = 45, d2 = ?
Example
Find the missing value m1 = 24, d1 = 30, m2 = 45, d2 = ?

9. Find the missing value x1 = 20, y1 = 7, x2 = 4, y2 = ?
Example
Find the missing value x1 = 20, y1 = 7, x2 = 4, y2 = ?

10. Questions

11. Assignment
Worksheet