How do you solve direct proportion questions?

This is best explained by giving an example.

If we are told that x is directly proportional to y^2, and when x=72, y=6, we may be asked to determine the relationship between x and y.

If x is directly proportional to y^2, we can say x=k(y^2), for some number k. We can then use the information we have about x=72 when y=6 to calculate k. If we substitute these values of x and y, we are left with 72 = k * 6^2, therefore 72 = k * 36, therefore k=2 and x = 2(y^2). We have determined the relationship between x and y and the question is now complete.

Note if '...' is directly proportional to '???', then ... = k ??? for some value k. Then we can use the information we have to solve for k and hence the relationship between ... and ???.

If x is directly proportional to y, then first write the following equation:

x = ky

Then look for the given value of y for a corresponding value of x and substitute them in the equation above and solve to find k.

I advise then rewriting the equation by replacing k with the number before going on to use the equation to complete the question.

Typically you will then be asked to find the value of x for a given value of y or vice versa which involves substituting the given value and solving the equation.