# Is yz = 5x an inverse variation?

Jul 24, 2015

It depends on which variables you are talking about. $y$ and $z$ are inversely proportional to each other, but $x$ and $y$ as well as $x \mathmr{and}$z# are directly propotional to each other.

#### Explanation:

$y$ and $z$ are inversely proportional to each other since $y z = 5 x$ implies that $y = \frac{5 x}{z}$ (an $z = \frac{5 x}{y}$). Therefore, the equation $y z = 5 x$ defines and inverse variation relative to $y$ and $z$.

On the other hand, since $x = \frac{1}{5} y z$, the original equation defines a direct variation (proportionality) between $x$ and $y$ and between $x$ and $z$.

A couple practical consequences of these facts:

1) If $z$ doubles, then $y$ will be cut in half. If $z$ triples, then $y$ will be cut by a third. Etc...

2) If $y$ or $z$ double (one or the other, not both), then $x$ will double. If $y$ or $z$ triple (one or the other, not both), then $x$ will triple. Etc...