Parallel and Perpendicular Lines

Parallel lines are coplanar lines that never intersect.

In two dimensions, parallel lines have the same slope.

Example:

The two lines

y = 3x + 8

y = 3x – 4

are parallel, since they both have slope 3.

 

Perpendicular lines are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines, you get –1.

Example:

The lines

are perpendicular, since

Exception: A horizontal line and a vertical line are perpendicular, even though the product of their slopes is undefined.