Suppose that a and b vary inversely and that b=5/2 when a=12. write a function that models the inverse variation. explain how you did it, !

Inverse variation means that y=k/x, or in this case a=k/b where k is the constant of proportionality (direct variation means y=kx) so:

a=k/b

We are told that b=5/2 when a=12 so we can solve for k

12=k/(5/2)

12=2k/5

60=2k

30=k

So the equation relating a to b is:

a=30/b or if you prefer

ab=30

Just a second zzz