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**Direct and Inverse Variation**

Day 2

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General Equation The general equation for direct variation is k is called the constant of variation.

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Example If y varies directly as x, and y=24 and x=3 find the constant of variation.

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Example y varies directly as x, and x=8 when y=9. Find the constant of variation. y = kx 9 = 8k k = 9/8

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**Example y varies directly as x, and x=8 when y=9. Find y when x = 4.**

Use the formula for direct variation. Y = 4.5

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**Inverse Variation y varies inversely as x if such that xy=k or**

Just as with direct variation, a proportion can be set up solve problems of indirect variation.

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Indirect Variation Lets do an example that can be solved by using the equation and the proportion.

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Solve: Find x when y=27, if y varies inversely as x and x=9 when y=45. Answer: 15

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**Determine if the chart is a direct variation**

x 10 12 14 16 18 y 20 24 28 32 36 To solve, find the constant of variation for each pairing of numbers using the formula y=kx. YES! The constant of variation is 2.

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**Determine if the chart is a direct variation**

x 20 16 12 8 4 y 10 6 2 To solve, find the constant of variation for each pairing of numbers using the formula y=kx. YES! The constant of variation is 1/2.

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**Determine if the chart is a direct variation**

x 6 9 15 18 24 y 2 3 5 12 To solve, find the constant of variation for each pairing of numbers using the formula y=kx. NO! The constant of variation is changes and is not the same for all pairs.

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**Determine if the charts are direct variations**

x 2 8 9 14 18 y 6 24 27 42 54 x -3 9 15 18 -21 y -2 6 10 12 -14 x -1 3 5 8 10 y -2 6 12 -14

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