it will have to be. See suppose you got the reqd line L. Then you can rotate it in such way that it just does not touch a red and a blue point. This line and L is doing same thing. So you can always find that line using the method i said
@pk301 Ok suppose you have a line that does not touch any point and you have a answer. You can rotate the line as much as you want without touching the point and the answer remains the same. So you need not consider the infinite possible lines. Just consider the ones close to the points and the answer you will get from the lines that are possible between the two points is the same!
consider point (x1, y1+delta1) and point (x2, y2-delta2).
now the line (y-y1+delta1)/(x-x1) = (y2-delta2-y1)/(x2-x1) will not have integer values to satisfy the equation. So, its safe to consider that the above line passes just above the point(x1,y1) and just below the point (x2, y2), and not intersection any other integer points in the plane.
not precisely my idea. Actually what i had done is rotated my reqd line and made it just touch a red or a blue point such that no point crosses that line. There will always be one such line out of infinite possibilities. Thats the line i choose