# Do all vertical lines have a slope of zero?

No, in some sense they have no slope, but if you'd want to assign a slope to it, it would be $\pm \infty$.
Almost every line on an $x , y$ plane can be described by $y = a x + b$. 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 $y = a x + b$ 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 $y = a x$ 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 $\pm \infty$, you would get the vertical line.