Direct Variation and Inverse Variation Finding the Missing Values

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

• 121

• 4

• 100

• 6

Is the given table a direct or inverse variation? What is the constant of variation?

• Direct, 12

• Inverse, 12

• Direct, 1/12

• Inverse, 1/12

Assume y varies inversely with x. If x=7 when y=4, what is y when x=2 ?

• 4

• 14 

• 7

• 28

Write an equation for this relationship.

• y=4x

• y=1/8x

• y=1/4x

• y=8x

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

• Yes; 1/4

• Yes; 4

• Yes; 2

• No

The width of a rectangle varies inversely with its length.  If the width is 6 when the length is 24, give an equation that shows the relationship.

• y = 4x

• y = 144x

• y = 4/x

• y = 144/x

The number of kilograms of water in a person’s body varies directly as the person’s mass.  A person with a mass of 90 kg contains 60 kg of water.  How many kilograms of water are in a person whose mass is 75 kg?

• 50 kg water

• 72 kg water

• 94 kg water

• 150 kg water

y varies directly with the square of x.  If y=40 when x=4, find y when x = 7

• 17.5

• 70

• 122.5

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

y varies directly as the square of x and indirectly with z. If y is 8 when x is 4 and z is 6, find y when x is 8 and z is 4.

• 3

• 12

• 48

• 64