September 6 Direct Variation

DIRECT VARIATION x is directly proportional to y x varies directly as yY X

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

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

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

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

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

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 What is the constant of variation? 4 The constant of variation is the reduced fraction. y = 4x

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.

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

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?

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.

8.2 Inverse Variation

INVERSE or indirect VARIATION y is inversely proportional to x y varies inversely as x K is the constant of variation or constant of proportionalityX Y

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

Inverse Variation When you buy a car, as time (t) increases, the value (v) decreases.tv 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.

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

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.

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