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.
