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Direct and Inverse Variation

Direct and Inverse Variation. Algebra I. Direct Variation. When the line passes through the origin. When y increases, x increases. Equation: y = kx , where k 0. Constant of variation – k Say “ y varies directly with x”. Identifying the constant of variation. y = 6x

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Direct and Inverse Variation

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  1. Direct and Inverse Variation Algebra I

  2. Direct Variation • When the line passes through the origin. • When y increases, x increases. • Equation: y = kx, where k 0. • Constant of variation – k • Say “ y varies directly with x”

  3. Identifying the constant of variation y = 6x 6 is the constant of variation (k) These can be graphed on the calculator using ‘y=‘ button, to see what the graph should look like.

  4. Examples: y = 28, x = 7 find x when y = 52 y = kx y = kx 28 = k(7)52 = 4x 7 7 4 4 4 = k 13 = x y = 4x

  5. Example: y = 27, x = 6 find x when y = 45

  6. Example: y = 27, x = 6 find x when y = 45 27 = k(6) 45 = 9/2x 6 6 (2/9)45 = x 9/2 = k 10 = x Y = 9/2x

  7. Example: y = -7, x = -14 find y when x = 20

  8. Example: y = -7, x = -14 find y when x = 20 -7 = k(-14) y = (½)20 -14 -14 y = 10 ½ = k y = ½x

  9. Inverse (Indirect) Variation • Line going away from the origin. • When one value (x or y) increases, the other value (x or y) decreases. • Equation xy = k • Say “y varies inversely as x” or “y is inversely proportional to x”.

  10. Different forms of the equation xy = k Y = k/x or x = k/y

  11. Example: If y = 12 when x = 5, find y when x = 3 xy = k 3y = 60 (5)(12) = k 3 3 60 = k y = 20 xy = 60

  12. Example: If y = 7, when x = -2; find y when x = 7 If y = 8.5, when x = -1; find x when y = -1 If y = 8, when x = 1.55; find x when y = -0.62

  13. Example: If y = 7, when x = -2; find y when x = 7 xy = -14 y = -2 If y = 8.5, when x = -1; find x when y = -1 xy = -8.5 x = 8.5 If y = 8, when x = 1.55; find x when y = -0.62 xy = 12.4 x = -20

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