y is inversely proportional to x. When y = 2, x = 3. Work out the value of y when x = 18.

We have that y is inversely proportional to x, which we write mathematically as y ∝ 1/x. We need to be able to solve this, so we re-write this expression as an equations, y = k/x, where k is the constant of proportionality. That means, for this relationship between x and y, k is always the same value (a constant). First, we need to find the value of k. To do this, we look for the 'pair' of x and y given in the question. This is a matching set of a given x and corresponding y value. In this question, we are told that when y = 2, x = 3. Subbing these into our equation, to leave k as the only known variable, we get 2 = k/3. We can rearrange this (multiply both sides by 3) to get k;k = 2 x 3 = 6. So our k value is 6. We can rewrite our generic proportionality equation for this case as y = 6/x. Now we can find the value of y when x = 18. Putting x = 18 into the equation y = 6/x, we have y = 6/18. Simplifying the fraction gives us y = 1/3.