Direct and Inverse Variation

Increases

If x and y vary inversely, as x decreases, what happens to the value of y?

Decreases

If x and y vary inversely, as y increases, what happens to the value of x?

y = 40

If y varies directly with x, and if x = -7 when y = -14, find y when x = 20.

k=2

If y varies directly with x, find the constant of variation if x = -7 when y = -14

y = 3x

If y varies directly with x, write an equation when y is 12 and x is 4.

y = 5x

If y varies directly with x, write an equation when y is 35 and x is 7.

75

The number of revolutions (R) made by a tire traveling over a fixed distance varies inversely with the radius of the tire (T). A 12-inch radius tire makes 100 revolutions to travel a certain distance. How many revolutions would a 16-inch radius tire require to travel the same distance?

12

The volume (V) of a gas kept at a constant temperature varies inversely with the pressure (P). If the pressure is 24 pounds per square inch, the volume is 15 cubic feet. What will the volume be when the pressure is 30 pounds per square inch?

y = 2x

Write the equation of variation: If y varies directly with x, find the constant of variation if x = -7 when y = -14.

y = 3800/x

Write the equation of variation: If y varies inversely with x, find the constant of variation if x = 38 when y = 100.

constant of variation

the "k" in direct and inverse variation equations

x = -128

y varies inversely with x. If y = 40 when x = 16, find x when y = -5

y = -5.6

y varies inversely with x. If y = 7 when x = -4, find y when x = 5

Direct

Are the given values Direct, Inverse, or Neither?

Inverse

Are the given values Direct, Inverse, or Neither?

y = kx

Direct Variation Equation

x = 2

If y varies inversely with x and x=-5 when y=-4.1, find x if y=10.25.

y = 50

If y varies inversely with x, and x = 38 when y = 100, find y when x = 76.

y = 15

If y varies inversely with x, and x = 9 when y = 45, then find y when x = 27.

k = 3800

If y varies inversely with x, find the constant of variation if x = 38 when y = 100

y = 48/x

If y varies inversely with x, write an equation when y is 12 and x is 4.

y = 21/x

If y varies inversely with x, write an equation when y is 3 and x is 7.

y = k/x

Inverse Variation Equation

1,000

The number of boxes (B) that a warehouse can store varies inversely with the average size (S) of the box. A warehouse can store 3,000 boxes when the average size of a box is 2 cubic meters. If the box size is now 6 cubic meters, how many boxes can the warehouse store?

20

The number of hours (H) needed to assemble computers varies directly with the number of computers (C). If 12 computers can be assembled in 9 hours, how many computers can be assembled in 15 hours?