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Chapter 2 Section 3 Direct Variation

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Writing and Interpreting a Direct Variation Direct Variation – a linear function defined by an equation of the form y = kx, where k 0 Constant of Variation, k, the ratio of y : x (usually written as a fraction )

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Identifying a Direct Variation from a Table For each function, determine whether y varies directly with x. If so, find the constant of variation and write the equation. a) xy b) xy Since the fractions are equal, the constant of variation (k) is 4. The equation is y = 4x. Since the ratios are not equal this is not a direct variation. y does not vary directly with x.

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Identifying Direct Variation from an equation For each function determine whether y varies directly with x. If so, find the constant of variation. a) 3y = 2x b)y = 2x + 3 Does this fit the form of y = kx? y = 2/3 xSolve for y. Does this fit the form of y = kx? What is k? y does not vary directly with x

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Using Proportions You can use proportions to solve some equations that do not require the constant of variation. Solve: Suppose y varies directly with x and x = 27 when y = -51. Find x when y = -17.

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Homework P. 74 #

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