Its very simple.  If you have a point R with vector RS, you can determine if point P is above or below by taking the dot product of the vectors RS and RP.  If its positive, its above, negative, its below, and zero its on the line.  It requires just 2 multiplications and an addition.

EDIT: Actually wait, that doesn't work.  Let me revise that.

EDIT2: The correct formula was this:
(X2 - X1)*(Py - Y1) - (Y2 - Y1)*(Px - X1)

You can improve it slightly to this:
(X2 - X1)*(Py - Y1) + (Y1 - Y2)*(Px - X1)

That replaces a subtraction with an addition to speed it up.

Alternatively, if you have a line of equation A*x+B*y=C, and a point (x₀,y₀), you can compare A*x₀+B*y₀ to C. If it's greater, it's on one side, if it's less than, it's on the other side, and if it's equal, it's on the line.

Also, if you ever want the exact distance from a point to a line, you'd do abs(A*x₀+B*y₀-C)/sqrt(A^2+B^2). This works especially well if sqrt(A^2+B^2) is a known constant (typically 1, but when working with integers something like 256 might be better)