1. Algebra 1 • Direct and InverseVariations

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

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

4. 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 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. y = kx 21 = k(7) Now divide both sides by 7 to solve for k. 7 7 k = 3 The price per hotdog is $3. y = 3x You could use this model to find the price (y) for any number of hotdogs (x) you buy.

5. y (price) y = 3x . (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

6. 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

7. With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them. x1y1 = x2y2 Inverse Variation

8. If y varies inversely with x and y = 12 when x = 2, find y when x = 8. x1y1 = x2y2 2(12) = 8y 24 = 8y y = 3 Inverse Variation

9. If y varies inversely as x and x = 18 when y = 6, find y when x = 8. 18(6) = 8y 108 = 8y y = 13.5 Inverse Variation

10. 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. Notebook Quiz