Is this equation #-12x = 6y# a direct variation and if so, what is the constant?

Answer 1

Yes, it represents a direct variation because variables #x# and #y# have constant ratio.

To demonstrate this, divide both sides of an equation by the same number #6#. This is an invariant transformation into an equivalent equation #y=-2x# from which follows that the constant of variation equals #k=-2#.

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Answer 2

Eva Adamson

Yes, the equation (-12x = 6y) is a direct variation because it can be rewritten in the form (y = kx), where (k) is the constant of variation. To find (k), solve the equation for (y):

[6y = -12x]

Divide both sides by 6:

[y = -2x]

Thus, the constant of variation (k) is (-2).

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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.