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Understanding Direct and Inverse Variation in Math

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Learn about direct and inverse variation relationships in mathematics, understand the concepts and how to apply them in equations. Practice problems included for better comprehension.

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Understanding Direct and Inverse Variation in Math

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  1. Direct Variation September 6

  2. X Y DIRECT VARIATION x is directly proportional to y x varies directly as y

  3. Direct Variation • y = kx • k is the constant of variation • the graph must go through the origin (0,0) and must be linear!! • Therefore it must be in y = kx form. The y-intercept is 0

  4. Example NonExample Direct Variation y = 3x y = .5x-1 y = 2/3x y = 5 y = 4 – 6x y = 11x y = 8.7x

  5. Direct Variation Ex 1)If x varies directly as y and x = 12 when y = 3, write an equation that relates x and y. Start with: y = kx Fill in x and y: 3 = k(12) Solve for k: Re-write equation with the k value: y = ¼ x

  6. Same problem, new ? Ex 1)If x varies directly as y and x = 12 when y = 3, find x when y = 10. y = ¼ x Fill in NEW x and y: 10 = ¼ (x) Solve for x: x = 40

  7. FIRST: what you are comparing NEXT: substitute your values correctly LAST: cross multiply to solve for missing variable. Another way to do the last ?

  8. 2) If y varies directly as x, and y = 28 when x = 7, find x when y = 52 write an equation that relates x and y. x = 13 The constant of variation is the reduced fraction. 4 What is the constant of variation? y = 4x

  9. 3) If y varies directly as the square of x, and y = 4 when x = 3, find y when x = 6 Use a proportion….. y = 16 write an equation that relates x and y.

  10. 4) A car uses 8 gallons of gasoline to travel 290 miles. How much gasoline will the car use to travel 400 miles? 11.034 gallons

  11. 5) In scuba diving the time (t) it takes a diver to ascend safely to the surface varies directly with the depth (d) of the dive. It takes a minimum of 3 minutes from a safe ascent from 12 feet. Write an equation that relates depth (d) and time (t). Then determine the minimum time for a safe ascent from 1000 feet?

  12. 6) z varies directly with x and y. z = kxy Write the equation relating x, y and z if x = 2, y = -6 and z = 24.

  13. Inverse Variation 8.2

  14. X Y INVERSE or indirect VARIATION y is inversely proportional to x y varies inversely as x K is the constant of variation or constant of proportionality

  15. Inverse Variation • This is a NON-LINEAR function (it doesn’t look like y=mx+b) • It doesn’t even get close to (0, 0) • k is still the constant of variation

  16. t v Inverse Variation When you buy a car, as time (t) increases, the value (v) decreases. The constant of variation, k is the amount that it decreases. t is the age of the car. v is the value of the car.

  17. Write the model that represents this situation. 6) If y varies inversely as x and when y = 12, x = 10.

  18. 7)The intensity of a light “I” received from a source varies inversely with the distance “d” from the source. If the light intensity is 10 ft-candles at 21 feet, what is the light intensity at 12 feet? Write your equation first.

  19. Work with partners on the WS HW: finish WS 5 show all work!

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