Direct, Inverse, Joint Variations

What is the constant (k) in this inverse variation?
y = 400/x

Mathematical Equivalence

ON

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

• 8 painters

• 10 painters

• 9 painters

• 11 painters

Suppose y varies directly as x.
If  y = 22.5 when x = 15, find y when x = 20.

• 1.5

• 337.5

• 30

• 16.875

The volume V of a gas kept at a constant temperature varies inversely as the pressure p. If the pressure is 40 pounds per square inch, the volume is 15 cubic feet. What will be the volume when the pressure is 30 pounds per square inch?

• 28 cubic feet

• 30 cubic feet

• 20 cubic feet

• 24 cubic feet

The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?

• 5.33 hours 

• 6.75 hours 

• 12 hours 

• 10 hours 

Which of the given graphs is a direct variation?

• A

• B

• C

• D

a varies inversely as the square of b. If a is 1 when b is 3, find a when b is 5. 

• 0.36

• 9

• 25

• 36

True or False:
An inverse variation is always a curve and a direct variation is always a line?

• True

• False

State what type of variation the equation represents.

• Direct

• Inverse

• Joint

• None

Is the given table a direct variation? If so, what is the constant of variation?

• Yes; 1/3

• Yes; 3

• Yes; 5

• No