Hmmmmmmmm. I shall post the original problem then. (The problem I posted was a smaller part of a larger problem).

Well m in terms of a and b is just

, right? Since the gradient of a line is given by change in vertical distance divided by change in horizontal distance?

And so the question evolves into:

I did it one way; i.e. assuming a and b are rational, and showing that this leads to a rational m. But it's the reverse way I can't show.

And by way of counterexample, you've shown that m rational doesn't necessarily imply a,b rational.

So have I simplified the problem incorrectly? Or is the original problem just incorrect?