9-2 Direct, Inverse, and Joint Variation

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9-2 Direct, Inverse, and Joint Variation Objective: To graph rational functions.

k is also called the constant of proportionality For example: The more hours you work the more money you get. The two are directly related. As one goes up, so must the other. In this example, what does k represent?

Example 1 If y varies directly as x and y = 9 when x is 15, find y when x = 21.

Example 2 If y varies directly as x, and y = 15 when x = 24, find x when y = 25.

Example 3 If a is directly proportional to b3, and a = 10 when b = 2, find a when b = 4.

Inverse Variation

If y varies inversely as x and y = 4 when x is 12, find y when x = 5.

Example If y varies inversely as x, and y = 22 when x = 6, find x when y = 15.

Example If m is inversely proportional to n, and m = 6 when n = 5, find m when n = 12.

If y varies jointly as x and z If y varies jointly as x and z. Then y = 80 when x = 5 and z = 8, find y when x = 16 and z = 2.

Example If z varies jointly as x and the square root of y, and z = 6 when x = 3 and y = 16, find z when x = 7 and y = 4.

Example If r varies jointly as s and t and inversely as u, and r = 18 when s = 2, t = 3, and u = 4, find s when r = 6, t = 2 and u = 4.

Assignment 9-2 pg 559 #18-28 even