Intuitively, it makes sense that one cannot assign a slope to a vertical line; a line that is "almost" vertical (i.e. is very steeply inclined) could have a very large positive or negative slope. So there is no way to decide even whether or not a vertical line should have positive or negative slope (and it clearly cannot have zero slope).
Two lines are parallel if they have the same slope. Parallel lines, when extended, do not intersect at any point.
Two lines are perpendicular if their slopes are opposite reciprocals of each other. For example, if a line has a slope of , a perpendicular line has a slope of - . Perpendicular lines intersect each other at right angles.