Question

Is `yz = 5x` an inverse variation?

Answer 1

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...