Almost every line on an #x,y# plane can be described by #y=ax+b#. Here #a# is called the slope of the line, and #b# is the y-coordinate where the line crosses the y-axis. If it has a slope 0, this would give #y=b#, so a horizontal line. Alternatively, every horizontal line has the form #y=b#, so a slope 0.

A vertical line is given by #x=c#, which can't be written as #y=ax+b# and has therefore no slope. However, you can apporximate a vertical line by taking a very steep line. For instance, if we take the ine #x=0#, we can approximate it by taking #y=ax# with #|a|# very large (#a# can be either negative or positive). So if you would make #|a|# larger and larger, you would approximate the line #x=0# to a better and better degree. So in some sense you could say that by taking the limit of #a# to #pmoo#, you would get the vertical line.