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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 1)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 y x

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Product Rule for inverse variation The product rule x 1 y 1 = x 2 y 2 can be used to solve inverse variation problems.

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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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