Is #7x+4y=2# a direct variation equation and if so, what is the constant of variation?

Answer 1

It is a direct variation is you can rewrite it in the form #y=m*x# where #m# is the constant.

We first bring the #y#'s to one side and the rest to the other, by subtracting #7x# from both sides: #4y=-7x+2#

Then divide both sides by 4: #y=-7/4x+1/2#

This is a linear equation, but according to my definition, this is not a direct variation, as there is allways this constant #1/2#. The graph of a direct variation should go through the origin: graph{7/4x+1/2 [-10, 10, -5, 5]}

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Answer 2

Kennedy Adams

No, the equation (7x + 4y = 2) is not a direct variation equation because it cannot be written in the form (y = kx). A direct variation equation must be in the form (y = kx) where (k) is the constant of variation.

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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.