 Solution

For $ax+by+c=0$, substitute $y=0$ or $x=0$, respectively:In terms of the original coordinates, these arewith each expression used only when its denominator is nonzero. If $a=0$, the straight line is horizontal: it misses the horizontal axis unless $c=0$, in which case it is that entire axis. If $b=0$, it is vertical: it misses the vertical axis unless $c=0$, in which case it is that entire axis. A straight line through the origin has both finite intercepts equal to the origin whenever neither axis is coincident with it.