What formula can represent ax-bx+y=0

The way you have written it now it is just a straight line. It is a bit weird that you have a and b, since you can rewrite as (a-b) x+y = 0, which shows that a-b is the constant that determines the slope of the line.

I suspect that you may have intended ax^2-bx+y=0. That is a parabola. But maybe not, and then it's just a straight line.

Your line will always pass through the origin (0,0). Regardless of a and b, you can easily (I hope) see that it will.

What is the question really asking?