Inverse Variation

*One element increases as the other decreases.

Are the following relationships examples of Direct Variation or Inverse Variation?

Ex.1 The mileage driven in a car and the amount of gas in the car’s gas tank.

Ex.2 Sea depth and its water temperature

Ex.3 The amount of hours you work at Wendy’s and your paycheck

Ex.4 The number of contractors building a deck and the amount of time it takes to build it

Ex.5 The outside temperature and the ice cream sales at Monkee Joes

Ex. 6

x y

1 10.00

4 2.50

8 1.25

20 0.50

Which statement about this relationship is true?

a. It is a direct variation because y = -2.5x + 12.5

b. It is an inverse variation because y = -2.5x + 12.5

c. It is a direct variation because 10 = xy

d. It is an inverse variation because 10 = xy

y

x

Ex. 7

An experiment is conducted on a container of gas that is kept at a constant temperature.

When the pressure on the gas is 30 pounds per square inch, the volume is 120 cubic inches.

When the pressure on the gas is 40 pounds per square inch, the volume is 90 cubic inches.

Let p represent the pressure on the gas.

Let v represent the volume of the gas.

Which statement is true about this relationship?

a. The volume of the gas varies directly with the pressure because v = 4p.

b. The volume of the gas varies directly with the pressure because vp = 3,600.

c. The volume of the gas varies inversely with the pressure because v = 4p.

d. The volume of the gas varies inversely with the pressure because vp = 3,600.

Ex. 8

Cost Per Person to Rent a Vacation Home

Number of People in Group Cost Per Person ($)

5 530.00

8 331.25

10 265.00

20 132.50

Which statement is true about this relationship?

a. It is a direct variation relationship because y = 2650x.

b. It is a direct variation relationship because

c. It is an inverse variation relationship because y = 2650x.

d. It is an inverse variation relationship because

Ex.9 Is this an inverse variation? _________ What is the constant of variation? __________

(-6, 8) (-4, 12) (-3, 16) (-2, 24) Write the equation: _____________________

Ex. 10 What is the other ordered pair for this inverse variation?_____ What is the constant of variation?______

(10, 10) (2, 50) (1, 100) (4 , ___) Write the equation: _____________________________