LAST CHAPTER!!!!!!! Yay!!!!!!!!! 8.1 & 8.2 Direct, Inverse & Joint Variation.

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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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Presentation transcript:

LAST CHAPTER!!!!!!! Yay!!!!!!!!! 8.1 & 8.2 Direct, Inverse & Joint Variation

Direct Variation “y varies directly as x” “y is directly proportional to x” “Direct” means “Divide”

Example 1 If y varies directly as x, and y = 15 when x = 24, find x when y = 25 Plug in x & y: Cross multiply & solve for x

Example 2 If a is directly proportional to b 3 and a = 10 when b = 2, find a when b = 4 Plug in a & b: Cross multiply & solve for a

Inverse Variation “y is inversely proportional to x” “y varies inversely as x” Inverse means Multiply

Example 3 If y is inversely proportional to x, and y = 6 when x = 5, find x when y = 12. Plug in x & y: Solve for x

Ex 4) Suppose that w varies directly as z 2 and inversely as x and y And that w = 10 when x = 15, y = 2, and z = 5. Find z when w = 2, x = 8, and y = 27. Plug in w, x, y, & z: Cross multiply & solve for z

Joint Variation “z varies jointly as x and y” “z is jointly proportional to x and y”

Example 5 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 Plug in x, y, z:

Example 6 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.

TOO If p varies inversely to the square root of q, and p = 12 when q = 36, find p when q = 16. Solve for p

Homework Pg. 354 #1-6 Pg #1-10