back of the napkin: take the first 4 points to be a unit box with the lower left point at the origin. You can draw any of 4 lines to the 5th point (x,y). Thes

back of the napkin: take the first 4 points to be a unit box with the lower left point at the origin. You can draw any of 4 lines to the 5th point (x,y). These 4 lines will have slopes x:y, x-1:y, x:y-1, x-1,y-1. You can always arrive at a slope ratio that is evenly divisible through some combination of -1 and reducing the ratio to simplest form. An evenly divisible slope ratio will pass through another point. example: 5th point (11,4). Choose line with slope 10:4. Divisible by 2, this line passes through the point (5,2). A ratio divisible by 3 would pass through 2 additional points etc.