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3.8 – Direct, Inverse, and Joint Variation

3.8 – Direct, Inverse, and Joint Variation. Direct Variation. When two variables are related in such a way that the ratio of their values remains constant. “y varies directly as x” would simply mean as x increases – so does y. Or as x decreases – so does y.

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3.8 – Direct, Inverse, and Joint Variation

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  1. 3.8 – Direct, Inverse, and Joint Variation

  2. Direct Variation • When two variables are related in such a way that the ratio of their values remains constant. • “y varies directly as x” would simply mean as x increases – so does y. Or as x decreases – so does y. • Form: y = kxn; n > 0, k is nonzero • k is called the constant of variation.

  3. The variables x and y vary directly and y=15 when x=3. a) Write the equation relating x and y.b) Find y when x = 9.

  4. The y varies directly as the cube of x and y=-67.5 when x=3. a) Write the equation relating x and y.b) Find x when y = -540.

  5. Inverse Variation • When the values of two quantities are related inversely proportional. • As one value increases, the other value decreases and vice versa • y = k/xn or xny= k , n > 0

  6. The variables x and y vary inversely when y = 14 when x = 3. a) Write the equation relating x and y.b) Find y when x = 9.

  7. Suppose y varies inversely with x2. When y = 15, x = 2. a) Write the equation relating x and y.b) Find y when x = 5.

  8. Joint Variation • A variation when one or more quantities vary directly as the product of two or more other quantities. • y = kxnzn; x and z are nonzero and n > 0

  9. Example 1 If y varies jointly as x and the cube of z and y = 16 when x = 4 and z = 2, find y when x = -8 and z = -3

  10. Example 2 If y varies jointly as x and z and inversely as the square of w, and y = 3 when x = 3, z = 10, and w = 2, find y when x = 4, z = 20, and w = 4.

  11. Homework 3.8 page 194 # 15, 18, 20

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