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