How do you write a direct variation equation that relates x and y if y = -8 when x = -2 then how do you find x when y = 32?

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Answer 1 · 2018-07-04T03:08:58

$x = 8$ when $y = 32$

Given: $x$ varies directly to $y$ . If $y = -8$ when $x = -2$ find $x$ when $y = 32$

Direct variation: $y = kx$ , where $k$ is the constant of proportionality

Find $k:" " -8 = k(-2)$

$k = (-8)/(-2) = 4$

$y = 4x$

Find $x$ when $y = 32$ :

$32 = 4x$

$x = 32/4 = 8$

CHECK using another method where you don't need to find $k$ :

$y_1/y_2 = x_1/x_2$

$(-8)/(32) = (-2)/x_2$

Use the cross-product to find $x_2$ , $x$ when $y = 32$ :

$-8 x_2 = -2(32)$

$-8x_2 = -64$

$x_2 = (-64)/(-8) = 8$