2. Direct and Inverse Variations

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

4. Direct Variation Direct variation uses the following formula:

5. Direct Variation example: if y varies directly as x and y = 10 as x = 2.4, find x when y =15. what x and y go together?

6. Direct Variation If y varies directly as x and y = 10 find x when y =15. y = 10, x = 2.4 make these y 1 and x 1 y = 15, and x = ? make these y 2 and x 2

7. Direct Variation if y varies directly as x and y = 10 as x = 2.4, find x when y =15

8. Direct Variation How do we solve this? Cross multiply and set equal.

9. Direct Variation We get: 10x = 36 Solve for x by diving both sides by 10. We get x = 3.6

10. Direct Variation Let’s do another. If y varies directly with x and y = 12 when x = 2, find y when x = 8. Set up your equation.

11. Direct Variation If y varies directly with x and y = 12 when x = 2, find y when x = 8.

12. Direct Variation Cross multiply: 96 = 2y Solve for y. 48 = y.

13. 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.

14. 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

15. 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

16. 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