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Understanding Direct, Inverse, and Joint Variation Relationships in Math

Learn about direct, inverse, and joint variation with practical examples and step-by-step solutions. Master solving for variables in different types of variations. Get ready for your final chapter exam!

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Understanding Direct, Inverse, and Joint Variation Relationships in Math

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  1. 8.1 & 8.2 Direct, Inverse & Joint Variation LAST CHAPTER!!!!!!! Yay!!!!!!!!! 

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

  3. 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

  4. Example 2 If a is directly proportional to b3 and a = 10 when b = 2, find a when b = 4 Plug in a & b: Cross multiply & solve for a

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

  6. 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

  7. Ex 4) Suppose that w varies directly as z2 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

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

  9. 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:

  10. 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.

  11. 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

  12. Homework • Pg. 354 #1-6 • Pg. 360-361 #1-10

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