2. Algebra 1 Direct and Inverse Variations

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

4. 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.

5. 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.

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

7. 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.

8. 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

9. 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) = 8y 24 = 8y y = 3

10. Inverse Variation 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

11. 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.