Algebra 1 Direct and Inverse Variations Objective Students

Algebra 1 Direct and Inverse Variations

Objective § § Students will understand the difference between direct and inverse variation. Students will compute both direct and inverse variation.

Direct Variation When we talk about a direct variation, we are talking about a relationship where as x increases, y increases at a CONSTANT RATE.

The price of hot dogs varies directly with the number of hotdogs you buy You buy hotdogs. x represents the number of hotdogs you buy. y represents the price you pay. y = kx 21 = k(7) 7 7 Let’s figure out k, the price per hotdog. Suppose that when you buy 7 hotdogs, it costs $21. Plug that information into the model to solve for k. Now divide both sides by 7 to solve for k. k=3 The price per hotdog is $3. y = 3 x You could use this model to find the price (y) for any number of hotdogs (x) you buy.

y (price) y = 3 x . . (3, 9) When you buy 3 hotdogs, you pay $9 (2, 6) When you buy 2 hotdogs, you pay $6 (1, 3) When you buy 1 hotdog, you pay $3 x (number of hotdogs) (0, 0) When you buy 0 hotdogs, you pay $0

Inverse Variation Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. There is not necessarily a constant rate.

Inverse Variation With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them. x 1 y 1 = x 2 y 2

Inverse Variation If y varies inversely with x and y = 12 when x = 2, find y when x = 8. x 1 y 1 = x 2 y 2 2(12) = 8 y 24 = 8 y y=3

Inverse Variation If y varies inversely as x and x = 18 when y = 6, find y when x = 8. 18(6) = 8 y 108 = 8 y y = 13. 5

Notebook Quiz § § Please take out a sheet of paper and put the proper school heading on the upper left of the paper. You may use your notebook and notes for this quiz.