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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?

Answer 1

Eli Assouline

#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#

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Answer 2

Julia Adams

To write a direct variation equation, use the form y = kx, where k is the constant of variation. Substitute the given values (-2, -8) into the equation to solve for k. Once you find k, substitute it into the equation and the given value of y (32) to solve for x.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.