Direct, Inverse, Combined, Joint Variation

This is a variation where one quantity varies directly to other quantity and inversely to the other quantity.

• Direct Variation

• Inverse Variation

• Joint Variaiton

• Combined Variation

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

• yes, the constant of variation is 1/2

• yes, the constant of variation is 2

• no, there is constant of variation.

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

• Yes; 1/3

• Yes; 3

• Yes; 5

• No

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

• yes, the constant of variation is 8.

• no, there is no constant of variation

• yes, the constant of variation is 1/8

If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k? 

• 121

• 4

• 100

• 6

In a direct variation, y = 39 when x = 3. 
Find the value of y when x = 2.

• 26

• 3

• 58.5

• 2

State what type of variation the equation represents.

• Direct

• Inverse

• Joint

• None

State what type of variation the equation represents.

• Direct

• Inverse

• Joint

• None

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

The variable x is in joint variation with y and z. When the values of y and z are 4 and 6, respectively, x is 72. What is the value of x when y = 2 and z =8?

• 32

• 48

• 64

• 96