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2-3 Direct Variations

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Direct Variation: y = kx y varies directly with x y varies directly as x k = constant of variation = slope The graph of a direct variation ALWAYS goes through (0,0), the origin K is never 0. K can be positive or negative.

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Direct Variation or not? Solve for y Put the equation in the form y = kx Does y vary directly with x? If so, find k. 1. 2x – 3y = 1 2. 2x – 3y = 0

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3. ½ x + 1/3y = 0 4. 7y = 2x 5. 3y + 4x = 8

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Write and solve a direct variation Use the given x and y values to find k. Rewrite your equation with the value for k and the x and y variables.

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Suppose y varies directly as x, and y = 9 when x = -3. Use the direct variation equation to find x when y = 15. Write a Direct Variation Equation

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If y = 2 2 / 3 when x = ¼,find y when x= 1 1 / 8 If y =4 when x =12, find y when x = -24

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Data Tables y = kx also equals y/x = k If k (constant of variation) is the same for each y divided by x, then you have a direct variation.

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Determine if each data table represents a direct variation. If so, write the equation. XY -23.2 12.4 41.6

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XY 46 812 1015

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XY -21 2 4-2

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XY 2 12 2-4

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Write the direct variation equation that goes through each point. Use (x,y) in y=kx. Find k, write your equation. 1) (1,2) 2) ( -3, 14)

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