1. 3.4 – Slope & Direct Variation

2. Direct Variation:

3. 3.4 – Slope & Direct Variation Direct Variation: y = kx

4. 3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation)

5. 3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads:

6. 3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads: “y varies directly with x.”

7. 3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads: “y varies directly with x.” –Direct Variation Equations ALWAYS go through the origin!!!

8. 3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads: “y varies directly with x.” –Direct Variation Equations ALWAYS go through the origin!!! –Constant of Variation = Slope

9. 3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads: “y varies directly with x.” –Direct Variation Equations ALWAYS go through the origin!!! –Constant of Variation = Slope, so k = m!

10. Ex. 1 Graph y = 4x

11. 1)Write the slope as a ratio.

12. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 =

13. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1

14. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0)

15. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0)

16. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point.

17. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 4

18. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 1 4

19. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 1 4

20. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 4)Draw line through points 1 4

21. Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 4)Draw line through points 1 4

22. Ex. 2 Graph y = -½x

23. 1)Write the slope as a ratio. 2)Graph (0,0) 3)Use slope to find next point. 4)Draw line through points

24. Ex. 2 Graph y = -½x 1)Write the slope as a ratio. 2 2)Graph (0,0) 3)Use slope to find next point. 4)Draw line through points 2

25. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.

26. Ex.3 If y = 8 when x= 4, find y when x= 5.

27. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation:

28. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx

29. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4)

30. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k

31. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2

32. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x

33. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x 2)Plug in given value, solve for missing!

34. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x 2)Plug in given value, solve for missing! y = 2x

35. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x 2)Plug in given value, solve for missing! y = 2x y = 2(5)

36. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x 2)Plug in given value, solve for missing! y = 2x y = 2(5) y = 10

37. Ex.4 If y = 36 when x = 6, find x when y = 42

38. 1)Write equation: 2)Plug in given value, solve for missing!

39. Ex.4 If y = 36 when x = 6, find x when y = 42 1)Write equation:y = kx 36 = k(6) 36 = 6k k = 6, so y = 6x 2)Plug in given value, solve for missing! y = 6x 42 = 6x 7 = x