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3.4 – Slope & Direct Variation

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

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3.4 – Slope & Direct Variation

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  1. 3.4 – Slope & Direct Variation

  2. 3.4 – Slope & Direct Variation • 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. Ex. 1 Graph y = 4x • Write the slope as a ratio.

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

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

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

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

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

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

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

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

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

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

  22. Ex. 2 Graph y = -½x

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

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

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

  26. 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.

  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. • 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. • 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. • 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. • 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. • 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. • 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. • Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x • 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. • Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x • 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. • Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x • 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. • Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x • 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. Ex.4 If y = 36 when x = 6, find x when y = 42 • Write equation: • Plug in given value, solve for missing!

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

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