direct and inverse variations

Direct and Inverse

Variations

Variation in general , will concern two variables; say height and weight of a person, and how , when one of these changes, the other might be expected to change.

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 We have Direct Variation, if the two

variables change in the same sense, that is, if one increases, so does the other.

An increase or decrease in one quantity with a corresponding increase or decrease in another quantity such that the ratio remains constant is called direct variation.

Direct Variation

y1x1

y2x2

Direct variation uses the following formula:

Direct Variationexample:

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 VariationIf 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

10

2.415

x

Direct Variation

How do we solve this? Cross multiply and set equal.

10

2.415

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 = 2ySolve 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 When two quantities vary inversely,

an increase in one leads to the decrease in the other quantity and vice-versa, in inverse ratio.

We have inverse variation if one going up causes the other to go down. An example of this might be speed & time to do a particular journey.

Inverse Variation

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

x1y1 = x2y2

Inverse VariationIf 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