2. Homework (Tuesday, 11/17) Lesson 3.08 packet http://www.virtualnerd.com/algebra-1/linear-equation-analysis/direct-variation/direct- variation-definition/constant-of-variation-definition

3. Per 3: Extra Credit for no missing assignments Trevor, Jonathan, Angie, Briana, Paul, Teo, Arenui, Maya, Karen, Arman, Pejhon, Naylie, Victoria, Jamie

4. Per 4: Extra Credit for no missing assignments Hamzeh, Francisco, Nathan, Arthur, Jose, Monaghan, Charli, Ashley, Alejandro, Daisy, Ava, Preston, Alexis, Ana, Katelyn, Sebastian, Oliver, Andrea

5. Per 5: Extra Credit for no missing assignments Azam, Sean B, Luis, Carly, Caroline G, Peyton, Karina, Kimberly, Nikki, Jennifer P, Abby, Sofia, Nan, Annabelle, Morgan, Jacob

6. Lesson 3. 08 Direct and Inverse Variations

7. Direct Variation a relationship where as x increases and y increases or x decreases and y decrease at a CONSTANT RATE. Formula: y = kx, where k cannot be zero and k is called constant variation

8. What does the graph y=kx look like? A straight line with a y-intercept of 0. y=3x

9. Looking at the graph, what is the slope of the line? Answer: 3 Looking at the equation, what is the constant of variation? Answer: 3 The constant of variation and the slope are the same!!!!

10. Direct Variation Direct variation uses the following formula:

11. Direct Variation Example 1: if y varies directly as x and y = 10 as x = 2.4, find x when y =15.

12. 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

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

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

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

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

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

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

19. Inverse Variation

20. In Inverse variation we will Multiply them. x 1 y 1 = x 2 y 2

21. What does the graph of xy=k look like? Let k=5 and graph.

22. This is a graph of a hyperbola. Notice: That in the graph, as the x values increase the y values decrease. Also, as the x values decrease the y values increase.

23. Inverse Variation Example 3: 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

24. Inverse Variation Example 4: 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