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

If  a  is inversely proportional to  b  then there is some constant  k  such that:  a  =  k / b.

 

Since  a = -6  when  b = 12     --->     -6  =  k / 12     --->    k  =  -6 · 12  =  -72.

 

For this problem, the formula is:  a  =  -72 / b.

 

When  b = -2     --->     a  =  -72 / -2  =  36.