Question

On a rectangle hyperbola, if one point is (2,3) and y varies inversely to x, find y when x is 6

Answer 1

The graph of y against x in inverse proportion is a rectangular hyperbola but I don't see at all how this knowledge/observation is any help in solving the problem.

Inverse proportion means that as x doubles y will halve and the equation is xy = k where k is some number. A good example of inverse proportion is speed and time taken over some fixed distance. In this case x could represent the speed (mph) and y the time (h) and then k is the distance in miles.

Since we know y=3 when x=2 we have xy = 6. Now it's easy to see when x=6 y=1.