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How does a computer distinguish an irrational number from a good, (necessarily rational) floating-point approximation of one?

The algorithm only works with points with integer coordinates, so the slope is always rational.

I think you have the last words because line drawing algorithms become irrelevant if you use a Floating Point Unit.

just:

{ x++ and y+=slope } or { y++ and x+= 1./slope }

Then slopes are always rational in line drawing algorithms.

If y and slope are floating point in the first block then might not y end at other than the desired endpoint because of accumulative error?