X is inversely proportional to Y. When X=4, Y=9. If Y=6, what is the value of X?

There are a few steps to this question. Before we can work out our value of X we will have to figure out an equation that links X and Y.Now if X were proportional to Y, then as X got bigger so would Y.We can write this as: X≈Y (≈ substitute for proportional symbol)However they are inversely proportional, meaning that as X increases, Y decreases.We can write this as: X≈1/Yor: X=k/YWhere k is a constant representing the rate of change that we don't yet know. The rate of change is the amount X will decrease as Y increases, and likewise the other way round. Now we have our basic equation, we need to figure out what our constant k is. We can do this using the X and Y values provided in the question (4,9). Using these, we can write the equation as:4=k/9 (multiply both sides by 9 to get rid of the division)9x4=k (resolve)36=k OR k=36So now we can rewrite our original equation with the new k value as:X=36/YThe final step, now that we have our equation, is to work out our new value of X when Y=6. To do this we just need to plug the Y value back into the equation. So:X=36/6 (solve)So X=6And that's the answer to the question. (Good job!)