1. Direct Variation A Type of linear function

2. Save for Monday 1.Find the rate of change, interpret in context! a)b) 2.

3. HW Check 1. 2. D3. B 1.Y = 1/32. y = 9/23. -9/2 1.Y = -x + 32. y = -1/3x – 1 3. Y = 2/3x + 24. y = 5/4x - 4

4. Puggly Wuggly Dollar Deals – Everything costs $1. Puggly Wuggly – Everything costs $2.50. Fancy Foods – Everything costs $4. Complete the investigation as we go!

5. Tables and Graphs xy Y=

6. Complete the tables for Puggly Number of Items x Puggly Wuggly Function _____*x Total Cost Y Number of Items x Fancy Foods Function _____*x Total Cost y 0 __________ __0 1 1 3 3 ________$20.00________$20.00 5 __________ __5 ________$42.50________$68.00 ________$252.50________$116.00

7. Recap What is direct variation? How does changing the cost of each item affect the graph? What do you notice is the same for each graph?

8. Anyone have a Job? http://www.pearsonsuccessnet.com/snpapp/iTe xt/products/0-13-068323-X/Ch05/05- 05/PH_Alg1_ch05-05_Obj1_vid1.html Thunderstorm in Toronto Canada http://www.youtube.com/watch?v=ikVN3B0R KlYhttp://www.youtube.com/watch?v=ikVN3B0R KlY

9. Direct Variation A function in the form y = kx, where k is the constant of variation. The variables y and x, “vary directly”! If The equation looks like y = kx, then it is DIRECT VARIATION!

10. Gulliver’s Travels

12. Is it DV? Is the equation Direct Variation? –Identify the constant k in each equation if it represents direct variation. 1. Y = 3x2. Y = 4x + 1 3. Y = x4. 2y = 8x 5. 5x + 2y = 06. 3x – y = 7 No JUNK in the TRUNK!

13. More facts about Direct Variation If the graph has the point (0,0), then it is DIRECT VARIATION!

14. Are these direct variation? a) b) c)

15. Writing a Direct Variation Equation Write a direct variation through the point (4, -3). Ex. 1: Write an equation of the direct variation that includes the point: (4, -3) Step1: Start with the direct variation equation: Step 2: Substitute the x and y in the ordered pair for the x and y in the equation. Step 3: Solve for k. Step 4: Write the equation substituting k (in step 3) for k in the equation

16. You try! 2. Write a direct variation through the point (5, 2) 3. Write a direct variation through the point (-6, -6) 4. Write a direct variation through the point (-3, -12)

17. Direct Variation in a Table The value of k must be the same for all points!

18. Do the values vary directly?

19. Proportions can also be used to solve DVs

20. Your distance from lightning varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see lightning, you are about 2 miles from the lightning. Write an equation for the relationship between time and distance.

21. C. Weight varies directly with gravity. With his equipment on an astronaut weighs 360 lbs on Earth but only 60 lbs on the moon. If another astronaut had landed on the moon that weighed 54 lbs with her equipment, how much would she weigh on Earth with equipment?

22. HW 4.3