11-3: Direct and Inverse Variation

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Presentation transcript:

11-3: Direct and Inverse Variation Models for Direct and Inverse Variation Direct Variation Inverse Variation y y x x x and y vary directly if for a constant k x and y vary inversely if for a constant k or or “division” “in line”

k is a constant of variation Ex 1: When x = 3, y = 12. Find an equation that relates x and y in each case. a.) x and y vary directly. “division” 1.) Find k. 2.) Write an equation. or

Ex 1: When x = 3, y = 12. Find an equation that relates x and y in each case. b.) x and y vary inversely. “in line” 1.) Find k. 2.) Write an equation. or

Ex 2: When x = 2, y = 4. Find an equation that relates x and y in each case. a.) x and y vary directly. “division” 1.) Find k. 2.) Write an equation. or

Ex 2: When x = 2, y = 4. Find an equation that relates x and y in each case. b.) x and y inversely. “in line” 1.) Find k. 2.) Write an equation. or

x 1 2 3 4 y 12 6 4 3 Inverse variation y x Ex 3: Decide if the data shows direct or inverse variation. Write an equation. x 1 2 3 4 y 12 6 4 3 Inverse variation y x

Ex 4: Decide if the data shows direct or inverse variation. Write an equation. x 1 2 3 4 y 2 4 6 8 Direct Variation y x

inverse variation direct variation Ex 5: State whether the variables have direct variation or inverse variation. 1.) The area B of the base and the height H of a prism with a volume of 10 cubic units are related by the equation BH = 10. inverse variation 2.) The velocity v of a falling object and the time t it has fallen are related by the equation 32t = v. consider direct variation