m = (y2 - y1) / (x2 - x1)
In order for this to be a vertical line, x2 - x1 would have to result in 0. In other words, if the denominator is 0, then it is a vertical line.
Just to let you know, if y2 - y1 results in 0 (if ur numerator is 0), then ur line will be horizontal.