What do you mean only integer arithmetic? Then you should probably represent the answer as rational number. The idea is as follows. Consider intersection of lines instead of intersection of segments (then check if point lies on both segments). Assume first line is given as set of points which look like and second line is solution of equation . Then you can find that for intersection point holds . After that you simply return for the value t you found.

Switching between distinct representations of lines should be an easy exercise for you.

P.S. You can also find the intersection point in algebraic way, solving system of two linear equations. This is straightforward but may yield a bit more of code.

P.P.S. You may refer to this article for more detailed explanation of basic analytic geometry stuff, including your question.

If you represent lines as equations like

ax + by = c
dx + ey = f

then intersection is the solution of the equation syste, which you can find using Cramer's rule, which means that you need to calculate 3 2x2 determinants A, B, C, and answers are A/C, B/C. Lines are parallel (or coincide) iff C=0