Section 3 Direct Variation

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Presentation transcript:

Section 3 Direct Variation Chapter 2 Section 3 Direct Variation

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 )

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. b) a) x y 1 4 2 7 5 16 x y 2 8 3 12 5 20 Since the ratios are not equal this is not a direct variation. y does not vary directly with x. Since the fractions are equal, the constant of variation (k) is 4. The equation is y = 4x.

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 y = 2x + 3 Does this fit the form of y = kx? y = 2/3 x Solve for y. Does this fit the form of y = kx? y does not vary directly with x What is k?

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.

Homework P. 74 # 1 - 27