If you follow many common steps for writing the equation of a line, you would start with the formula for slope. Since any vertical line has all points with the same "x" value, your slope slope has a denominator of zero. The slope, therefore, does not exist.

As a teacher, my advice to all students learning to write the equations of vertical and horizontal lines is to accept them as they are: special cases that deserve special attention (like learning idioms in a foreign language).