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What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems

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1) Direct Variation 2) Joint Variation 3) Inverse Variation

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Direct Variation Can be expressed in the form y=kx K in this equation is called constant of variation Slope of a direct variation = constant of variation. As x increases, y increases or decreases at a constant rate (y varies directly as x)

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If you know [y varies directly as x] and one set of values, you can use a proportion to find the other set of corresponding values.

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Joint Variation When 1 quantity varies directly as the product of two or more other quantities. Y varies jointly as x and z if there is some number k such that y=kxz

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If you know y varies jointly as x and z and one set of values, you can use a proportion to find the other set of corresponding values.

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Suppose y varies jointly as x and z. Find y when x=8 and z=3, if y=16 when z=2 and x =5. Joint Variation Cross Multiply Divide by 10 Substitute numbers into the Joint Variation

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Inverse Variation As one quantity increases, the other quantity decreases. If there is a nonzero constant k, xy=k or y= Speed and time vary inversely with each other because when you travel somewhere, as your speed increases, the time it takes you to get there decreases.

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Homework! =) Page 496 # 14-40 odd What is special about the # 496?

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Copyright © 2009 Pearson Education, Inc. Chapter 6 Section 5 – Slide 1 Chapter 4 Variation.

Copyright © 2009 Pearson Education, Inc. Chapter 6 Section 5 – Slide 1 Chapter 4 Variation.

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