Direct and Inverse

Variations

Direct Variation

Which of these tables models direct variation? If so, write an equation.

NO

Tell if the following graph is a Direct Variation or not.

No Yes

(straight line through the origin!)

No No

example:If y varies directly as x and y = 10 as x = 2.4, find x when y =15.

10

2.4

15

x10x = 36

x=3.6

If y varies directly with x and y = 12 when x = 2, find y when x = 8.

Cross multiply: 96 = 2ySolve for y. 48 = y.

12

2y

8

The Weight (V) of an object on Venus varies directly as its weight (E) on Earth. A person weighing 120 lb on Earth would weigh 106 lb on Venus. How much would a person weighing 150 lb on Earth weigh on Venus?

150(106) = 120y15900 = 120y

132.5 pounds =y

Inverse Variation

Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down.

The values of x and y always multiply to give the same value.

Graphs of inverse variation…

Which of these tables models indirect variation? If so, write an equation.

NO

Inverse Variation

With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them.

x1y1 = x2y2

Inverse Variation

If y varies inversely with x and y = 12 when x = 2, find y when x = 8.

x1y1 = x2y2

2(12) = 8y 24 = 8y y = 3

Inverse VariationIf y varies inversely as x and x = 18 when y = 6, find y when x = 8.

18(6) = 8y 108 = 8y y = 13.5

In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board.  If it takes 5 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it take to break a board that is 6 feet long?

10=6x

1.67 lbs=x