Direct and inverse variations
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Direct and Inverse Variations. 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. Direct variation uses the following formula:. example:

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Direct variation l.jpg

When we talk about a direct variation, we are talking about a relationship where as x increases, y increasesor decreases at a CONSTANTRATE.

Direct Variation


Direct variation3 l.jpg
Direct Variation a relationship where as

Direct variation uses the following formula:


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 l.jpg

example: a relationship where as

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


Direct variation5 l.jpg

If y varies directly as x and y = 10 a relationship where as 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




We get 10x 36 solve for x by diving both sides by 10 we get x 3 6 l.jpg

We get: 10x = 36 y =15

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 l.jpg

Let’s do another. y =15

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

Set up your equation.

Direct Variation



Cross multiply 96 2y solve for y 48 y l.jpg

Cross multiply: 96 = 2y when x = 8.

Solve for y. 48 = y.

Direct Variation


Inverse variation l.jpg

Inverse when x = 8. 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


Slide13 l.jpg

With when x = 8.Direct variation we Divide our x’s and y’s.

In Inverse variation we will Multiply them.

x1y1 = x2y2

Inverse Variation


Inverse variation14 l.jpg

If y varies inversely with x and when x = 8.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 l.jpg

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

Inverse Variation


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