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Direct Variation

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  1. Direct Variation

  2. y 4 3 2 1 -1 -2 -3 -4 x 1 2 3 4 -1 -2 -3 -4 Does the graph represent direct variation?

  3. NO

  4. Which line represents direct variation?

  5. K

  6. y x Does the graph represent direct variation?

  7. YES

  8. Which equation represents direct variation? A y = 2/3x + 5 B y = 5 C y = 2/3x D x = 2/3

  9. C

  10. Which equation represents direct variation? A y = -4x B y = -4x + 1 C y = -4 D x = -4

  11. A

  12. The amount of money earned on a job varies directly to the number of hours worked. If $50.00 is earned in 8 hours, how much is earned for 35 hours of work?

  13. M = kH 50.00 = 8k 6.25 = k M = 6.25H M = 6.25(35) M = 218.75

  14. 8x = 50(35) • 8x = 1750 • x = 1750/8 • x = 218.75 • $218.75

  15. A scale distance of 2.5 centimeters on a certain map represents an actual distance of 180 kilometers. If the distance on the map varies directly with the actual distance, what actual distance does 6.5 centimeters on the same map represent?

  16. S = kA 2.5 = k(180) 1/72 = k S = 1/72A 6.5 = 1/72A 468 = A

  17. 2.5x = 180(6.5) • 2.5x = 1170 • x = 1170/2.5 • x = 468 • 468 kilometers

  18. Mr. Johnstone used 15 gallons of gasoline to drive 450 miles. If the amount of gasoline used varies directly with the number of miles driven. How far can he drive on a full tank of 20 gallons?

  19. G = kM 15 = k(450) 1/30 = k G = 1/30M 20 = 1/30M 600 = M

  20. 15x = 450(20) • 15x = 9000 • x = 9000/15 • x = 600 • 600 miles

  21. Mr. Parker drove 143 mi in 3.25 hours. If the distance driven varies directly with the amount of time, how far would he travel in 5 hours?

  22. D = kT 143 = k(3.25) 44 = k D = 44T D = 44(5) D = 220

  23. 3.25x = 143(5) • 3.25x = 715 • x = 715/3.25 • x = 220 • 220 miles

  24. Distance, d, varies directly as time, t, when speed remains constant. If d is 240 miles when t is 8 hours, what is the constant speed?

  25. y = kx • d = st • 240 = 8s • 240/8 = s • 30 = s

  26. If m varies directly as p, and m = 5 when p = 7, what is the constant of variation?

  27. y = kx • m = kp • 5 = 7k • 5/7 = k

  28. The number of calories, n, a person burns varies directly with the amount to time, t, spent running. If n = 275 when t = 22, what is the constant of variation?

  29. y = kx • n = kt • 275 = 22k • 275/22 = k • 12.5 = k • 25/2 = k