Direct and Inverse Variation

direct variation definition

Linear function that uses the equation, y=kx, and always passes through the origin (0,0); typically, as x increases, y increases (EX: gallons of water used in shower)

105

Johnny makes $15 for every two days he delivers newspapers. How much would he make after two weeks?

direct variation

If a car uses 8L of gas to travel 160km, how much gas will the car use to travel 400km?

Inverse variation

It takes a factory 10 days to produce 10,000 cars. How many days would it take two factories to produce the same number of cars?

inverse variation definition

Non-linear function that uses the equation, y=k/x, and never passes through (0,0) or crosses the axes; typically, as x increases, y decreases (EX: cleaning desks)

180

Three pipes take 1 hour to water the football field. How many minutes would it take one pipe to water the field?

30

What is the constant of variation for y = k/x if x= 10 and y = 3?

3

What is the constant of variation for y = kx, if x = 6 and y = 18?

divide y/x

how to find the constant of variation (k) for a direct variation

multiply xy

how to find the constant of variation (k) for an inverse variation

constant of variation

k; shows the relationship between the x-value and y-value in direct and inverse variations

direct variation equations

y=3x; 4x+y=0; y=1/2x; y=0.4x; y=x/8; 2x=6y are examples of---

inverse variation equations

y=7/x; xy=9; y=-5/x are examples of---