Direct and Inverse Variations

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Presentation transcript:

Direct and Inverse Variations

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

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

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.

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

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

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 x1y1 = x2y2 2(12) = 8y 24 = 8y y = 3 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