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**Lesson 12.1 Inverse Variation pg. 642**

Objectives: To graph inverse variation. To solve problems involving inverse variation.

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Inverse Variation y varies inversely as x if there is some nonzero constant k such that xy = k

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**Inverse Variation Problems**

To solve some inverse variation problems, there are two steps: (1) First find the value of k (2) Use the value of k to find a specific value of x or y

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**Graphing Inverse Variation**

To graph inverse variation choose values for x and y whose product is k

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**Ex. 1: Graphing inverse variation**

Graph an inverse variation in which y varies inversely as x, and y=1 when x=4

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**Graph an inverse variation in which y varies inversely as x, and y=-6 when x=-2**

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**Product Rule for inverse variation**

The product rule x1 y1 = x2y2 can be used to solve inverse variation problems.

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**1. If y varies inversely as x and y = 5 when x =12, find x when y = 15**

Ex. 2: Write and inverse variation equation that relates x and y. Assume that y varies inversely as x. Then solve. 1. If y varies inversely as x and y = 5 when x =12, find x when y = 15

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**2. If y varies inversely as x and y = 8 when x =6, find y when x = 4**

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Direct variation Y = mX. Y X 1 2 3 4 5 6 7 8 9 10 number of sessions 40 35 30 25 20 15 10 5 0 Cost ($) The cost of private gymnastic lessons (y) varies.

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