Direct and InverseVariations

Name:- Manpreet Singh

Class:- VIII-J

Direct Variation

When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.

Direct Variation Direct variation uses the following

formula:

Direct Variation

example:

if y varies directly as x and y = 10 as x = 2.4, find x when y =15.

what x and y go together?

Direct Variation If y varies directly as x and y = 10

find x when y =15.

y = 10, x = 2.4 make these y1 and x1

y = 15, and x = ? make these y2 and x2

Direct Variation if y varies directly as x and y = 10 as x =

2.4, find x when y =15

Direct Variation How do we solve this? Cross multiply

and set equal.

10

2.4

15

x

Direct Variation

We get: 10x = 36

Solve for x by diving both sides by 10.

We get x = 3.6

Direct Variation Let’s do another.

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

Set up your equation.

Direct Variation

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

12

2y

8

Direct Variation

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

12

2y

8

Inverse Variation

Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. There is not necessarily a constant rate.

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 Variation If y varies inversely as x and x = 18

when y = 6, find y when x = 8.

18(6) = 8y

108 = 8y

y = 13.5

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