Is #yz = 5x# an inverse variation?

1 Answer
Jul 24, 2015

Answer:

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...