You only need to eliminate vertical lines where x = c. So if the first two points have the same x value, you only have to check that all subsequent points have the same x-value. Otherwise, havijng eliminated the exceptional case, you can process each pair of points (in any order! i.e. iterate the 2nd thru last comparing with iterator - 1) to ensure they produce consistent (throughout the loop) values for m and c in the simultaneous equation y1=m*x1+c and y2=m*x2+c.

BUT, if this is experimental data, you need to calculate the standard deviation from the line of regression instead, e.g. using Statistics::LineFit.

Update: I'd refer to zentara's Solving Simultaneous Equations with Matrices (use PM Supersearch) for the second part of the algorithm). And even if the data were not experimental, personally I'd go the Stats Line Fit route anyway because it is a tolerant solution to rounding errors.