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Inverse Variation

Inverse Variation is an equation in the form of xy = k, k0. k is the constant of variation. Algorithm ­ Writing an Equation 1. Write the equation xy = k 2. Substitute the values for x and y 3. Solve for k 4. Write the formula, xy = k, and substitute value of k.

1. 2.

Write an equation of inverse variation that includes the point (2, 4). Write an equation of inverse variation that includes the point (3, 15).

3.

Write an equation of inverse variation that passes through the point (­6, 1).

4.

Find the constant of variation that passes through the point (5, 7).

N.B. The product of the ordered pairs is always a constant in Inverse variations WORD TRANSLATION ­ y (dependent variable) varies inversely with x (independent variable). When reading a word problem, use the word translation above to determine your values of x and y to find the value of k, then write your equation of inverse variation. Use that equation to find other values of x or y.

Hanlonmath 800.218.5482 [email protected]

1.

In planning a trip, the time it takes to make the trip varies inversely with the rate of the car. If I take Route A and average 40 mph, it will take 9.5 hours to complete the trip. If I go by Route B and average 50 mph, how long will the tip take? At a constant temperature, the volume of gas is inversely proportional to the pressure applied to the gas. A closed tank contains 300 cubic feet of gs at an unchanging temperature. If the constant of variation is 6000, find the pressure in the tank.

2.

3.

The points (3, 8) and (2, y) are two points on the graph of an inverse variation. Find the value of y.

4.

The weight needed to balance a lever varies inversely with the distance from the fulcrum to the weight. Where should John, who weighs 150 lbs, sit from Barbara, a girl weighing120 lbs and six feet away from the fulcrum?

5.

The cost of gas for a trip is to be split among the people riding on the bus. If there are 10 people on the bus, the total cost of the trip for gas is $50. How much would each person have to pay for the trip if there were eight people on the bus?

Hanlonmath 800.218.5482 [email protected]

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