Question

Suppose that alpha is inversely proportional to beta. If alpha = -6 when beta = 12, find alpha when beta = -2.

Answer 1

36

Explanation:

Equation for an inversely proportional relation, where y is inversely proportional to x:

`y = (k)/(x)`

Here we have:

`\alpha = (k)/(\beta)`

We use the known ordered pair to find k.

`-6 = (k)/(12)`

`k = -72`

The relation is:

`\alpha = (-72)/(\beta)`

For beta = -2,

`\alpha = (-72)/(-2)`

`\alpha = 36`