Information about 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 y1 x1 = y2 x2 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 10 2.4 = 15 x

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 2 = y 8

Direct Variation Cross multiply: 96 = 2y Solve for y. 48 = y. 12 2 = y 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

Direct and Inverse Variation. y varies directly with x (or: "x and y are directly proportional") if there is a constant k such that (You can put the "k" on ...

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Sal explains what it means for quantities to vary directly or inversely, and gives many examples of both types of variation.

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Type: Resource Title * graphing calculator reference: Lesson: Direct Variation: Lesson: Inverse Variation: Practice: Practice Solving Direct and Inverse ...

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Direct variation describes a simple relationship between two variables. We say y varies directly with x (or as x, in some textbooks) if:

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Explains the basic terminology of variation problems, and demonstrates how to solve symbolic variation problems.

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Inverse Variation (The Opposite of Direct Variation) In an inverse variation, the values of the two variables change in an opposite manner ...

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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 ...

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Understanding direct and inverse variation Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/alge ...

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Fun math practice! Improve your skills with free problems in 'Identify direct variation and inverse variation' and thousands of other practice lessons.

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