Algebra 1 · Unit 5 · Topic 5.4
Parallel and Perpendicular Lines
Distinct nonvertical parallel lines have equal slopes.
Definition and explanation
Distinct nonvertical parallel lines have equal slopes. Nonvertical perpendicular lines with defined nonzero slopes satisfy m₁m₂ = −1; a horizontal line is perpendicular to a vertical line.
Worked example
A line perpendicular to y = 2x + 1 and passing through (4, 3) has slope −1/2. Thus y − 3 = (−1/2)(x − 4), or y = −x/2 + 5. Its slope product with 2 is −1.
Common mistake
Changing only the sign of a slope does not generally produce a perpendicular line.
Key takeaway
Distinct nonvertical parallel lines have equal slopes.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.