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Direct Variation

Direct Variation. Chapter 5.2. Direct Variation. Lesson Objective: NCSCOS 4.01 – Students will know how to solve problems using direct variation. Direct Variation. Equation of Direct Variation. y = kx. y = k x. Coefficient of Variation. Or:. Constant of Variation. Direct Variation.

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Direct Variation

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  1. Direct Variation Chapter 5.2

  2. Direct Variation • Lesson Objective: NCSCOS 4.01 – Students will know how to solve problems using direct variation

  3. Direct Variation • Equation of Direct Variation y = kx y = kx Coefficient of Variation Or: Constant of Variation

  4. Direct Variation • When you see: “y varies directly as x” write y = kx

  5. Direct Variation • Write the equation of direct variation that has a equal to -3 • Replace k with -3 coefficient of variation y = kx y = kx y = -3x

  6. Direct Variation • Write the equation of direct variation using the coefficient given: • K = 3 • K = -4 • K = 13 • K = • K = Practice 2 3 -5 7

  7. Direct Variation • Assume If the coefficient of variation is ½, then what is the value of y when x = -6? y varies directly as x. y = kx • Replace k with ½ • Replace x with -6 • Multiply ½ times -6 to get answer y= ½x y= ½(-6) y = -3

  8. Direct Variation • Assume y varies directly as x. If the coefficient of variation is 2, then what is y when x is 5? • Assume y varies directly as x. If the coefficient of variation is 1/2, then what is y when x is 8? • Assume y varies directly as x. If the coefficient of variation is -2/3, then what is y when x is -9?

  9. Direct Variation • Assume y varies directly as x. If the coefficient of variation is 4, then what is the value of x when y = 6? • Replace k with 4 and y with 6 • Divide 4 on both sides • Reduce the fraction 3 y = kx y = 4x 6 = 4x = x 4 4 2

  10. Direct Variation • Assume y varies directly as x. If the coefficient of variation is 2, then what is x when y is 5? • Assume y varies directly as x. If the coefficient of variation is 1/2, then what is x when y is 3? • Assume y varies directly as x. If the coefficient of variation is -1/3, then what is x when y is -2?

  11. Direct Variation • If y varies directly as x and y is 4 when x is -2, then what is the equation of direct variation? • Begin with: • We’re looking for k • Let’s solve this equation for k y = kx x x y k = x

  12. Direct Variation • If y varies directly as x and y is 4 when x is -2, then what is the equation of direct variation? • Plug in the x and y values • Reduce the fraction y k = x 4 k = -2 k = -2

  13. Direct Variation • Once you know k, plug it into our equation of direct variation • This is our equation: y = kx y = -2x

  14. Direct Variation • Assume y varies directly as x. If the y is 4 when x is 2, then what is the value of y when x = 6? • To find k we use: • When there are 3 numbers we’ll use a proportion. This looks like: y k = x y y = x x

  15. Direct Variation • Assume y varies directly as x. If the y is 4 when x is 2, then what is the value of y when x = 6? • Plug in the numbers • We then cross multiply y y = x x y 4 = 2 6 2y = 24

  16. Direct Variation 2y = 24 • Solve for y 2 2 y = 12

  17. Direct Variation • Assume y varies directly as x. If y is 9 when x is 3, then what is y when x is 2? • Assume y varies directly as x. If y is 3 when x is 9, then what is y when x is 15? • Assume y varies directly as x. If y is -8 when x is 2, then what is y when x is -3? • Assume y varies directly as x. If y is -6 when x is -14, then what is y when x is 7?

  18. Direct Variation • Assume y varies directly as x. If the y is 4 when x is 2, then what is the value of x when y = 6? • Plug in the numbers • We then cross multiply y y = x x 4 6 = x 2 4x = 12

  19. Direct Variation 4x = 12 • Solve for x 4 4 y = 3

  20. Direct Variation • Suppose y varies directly as x. If y = 3 when x = 15, then find x when y = 5. • Suppose y varies directly as x. If x = -8 when y = 24, then what is x when y = -2? • Suppose y varies directly as x. If y = -7 when x = -14, find x when y = 10 • Suppose y varies directly as x. If x = 15 when y = 12, find x when y = 21.

  21. Direct Variation Quiz! • Find the equation of direct variation if the coefficient of variation is -2/3. • Assume y varies directly as x. If the coefficient of variation is 3, then what is y when x is 4? • Assume y varies directly as x. If the coefficient of variation is -4, then what is x when y is -32? • Assume y varies directly as x. If y is 18 when x is -6, then what is y when x is 4? • Assume y varies directly as x. If y is -3 when x is 9, then what is x when y is -7?

  22. Direct Variation • It costs $2 per ringtone that you download for your cell phone. How much would it cost to download the following? 0 2 4 6 8

  23. Direct Variation 1 2 3 4 5 6 7 8 • Graph the results 1 2 3 4 5 6 # of Ringtones

  24. Direct Variation 1 2 3 4 5 6 7 8 • Notice that a pattern is forming • Connect the dots • Direct variation graphs always go through the origin! 1 2 3 4 5 6 # of Ringtones

  25. Direct Variation 1 2 3 4 5 6 7 8 • What is the slope of this equation? 2 1 1 2 1 2 3 4 5 6 # of Ringtones

  26. Direct Variation 2 4 6 8 10 12 14 • What is the equation of the graph? 1 2 3 4 5 6 # of Songs Downloaded

  27. Direct Variation • Find the slope of a line that passes through the origin and (3, 2). • Write the equation of variation if y is 2 when x is 3. • What do you notice about your answers to the two questions? • The slope and k are the same • Graph both of these problems

  28. Direct Variation 1 2 3 4 5 6 7 • Y = 2/3x 1 2 3 4 5 6 # of Songs Downloaded

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