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

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

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

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)

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.

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

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.

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

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.

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

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