What is the difference between slopes of parallel lines and slopes of perpendicular lines?

Slopes of parallel lines have the same slope (they are changing at the same rate).

Slopes of perpendicular lines have slopes that are the negative inverse of each other, that is, their product is -1. (The slope of a vertical line is therefore undetermined, not infinity. There is no slope s that times 0 equals -1.)

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Let m1 be the slope of line one and m2 be the slope of line two. Then:

• If the lines are parallel, then their slopes are equal, so m1 - m2 = 0.
• If the lines are perpendicular, then their slopes are negative inverses of each other, so

= m1 - (-1/m1)

= m1 + 1/m1

= (m12 + 1)/m1