2. Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?

3. Today we will be able to solve and graph Inverse Variation problems Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost? This is a direct variation problem. We set them up As a proportion and solve.

4. 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.

5. Direct Variation Direct variation uses the following formula:

6. 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?

7. 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

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

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

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

11. 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.

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

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

14. Inverse Variation Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. Can you think of an example Of this happening?

15. 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

16. 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

17. Inverse Variation If y varies inversely with x: X 482x Y 63y

18. Inverse Variation If y varies inversely with x and all Products =24 X 482X=-24 Y 63Y=12

19. 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

20. Graphing inverse variations- the graph is a hyperbola. xy = c where c is the product of x and y Ex: xy = 12 then

21. Example: If it takes 3 carpenters to frame a house in 8 weeks, how many weeks will it take four carpenters to frame the same house?

22. Example: If it takes 3 carpenters to frame a house in 8 weeks, how many weeks will it take four carpenters to frame the same house? (3)(8) = (4)(w) W =6

23. Exit ticket Create an inverse variation problem with your partner and hand it in on an index card for 3 bonus points on your next test!