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The question is the following:

The equation $3x+5y+7z=15$ can be rewritten as $z = \frac{15}{7} - \frac{3}{7}x-\frac{5}{7}y$. What are the meanings of the three fractions that appear in this equation?

I know that $\frac{15}{7}$ is the intersection of the plane on the $z$-axis. However, is $-\frac{3}{7}$ the slope on the $x$-axis and $-\frac{5}{7}$ on the $y$-axis? Any help will be appreciated.

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    $\begingroup$ That's basically it. If you increase the $x$ coordinate by $1$, you will increase the $z$ coordinate by $-\frac 37$ (assuming you stay on the plane of course). Edit: I'm not sure whether this has a proper name though. $\endgroup$
    – N.Bach
    Commented Apr 21, 2018 at 23:43
  • $\begingroup$ Thank you so much! $\endgroup$
    – geo_freak
    Commented Apr 23, 2018 at 0:07

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