3Writing and Interpreting a Direct Variation Direct Variation – a linear function defined by an equation of the form y = kx, where k ≠ 0Constant of Variation, k, the ratio of y : x (usually written as a fraction )
4Identifying 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)xy1427516xy28312520Since 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.
5Identifying Direct Variation from an equation For each function determine whether y varies directly with x. If so, find the constant of variation.a) 3y = 2xy = 2x 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 xWhat is k?
6Using ProportionsYou 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 = Find x when y = -17.