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Is $y=x-4$ a direct variation? If so, what is the constant of variation and the slope of the direct variation model?

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Yes. The slope is 1, and I believe the constant is -4. –  Potato Dec 6 '12 at 3:12
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To others: "direct variation" is a phrase used in some high school math textbooks (e.g. mine, unfortunately) to describe linear equations. –  Potato Dec 6 '12 at 3:13

2 Answers 2

If direct variation means that $y=kx$ for some constant $k$, then $y=x-4$ is not a direct variation.

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There is a direct relation between $x$ and $y$ whenever $m>0$ and $y=mx+b$. Then, $m$ is the slope and the constant of variation is $b$.

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