Is yz = 5x an inverse variation?

1 Answer
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 and z# are directly propotional to each other.

Explanation:

y and z are inversely proportional to each other since yz=5x implies that y=(5x)/z (an z=(5x)/y). Therefore, the equation yz=5x defines and inverse variation relative to y and z.

On the other hand, since x=1/5 yz, 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...