Direct and Inverse Variation

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Presentation transcript:

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 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.

Examples: y = 28, x = 7 find x when y = 52

Examples: y = 28, x = 7 find x when y = 52 y = kx y = kx

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

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

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

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

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

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”.

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

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

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

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