Parallel and Perpendicular Lines
A free College Algebra lesson from the “Graphs and Forms of Linear Equations” unit, with a worked example and practice problems including step-by-step solutions.
Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals, unless one line is vertical and the other horizontal.
What you'll learn
- Identify parallel slopes
- Identify perpendicular slopes
- Write related line equations
Worked example
Problem. What slope is perpendicular to 2/3?
- Flip 2/3 to get 3/2.
- Change the sign.
- The perpendicular slope is -3/2.
Answer: -3/2
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. What slope is parallel to -5?
Show solution
- Parallel slopes match.
Answer: -5
2. What slope is perpendicular to 4?
Show solution
- Use the opposite reciprocal.
Answer: -1/4
3. What slope is perpendicular to -2/7?
Show solution
- Flip and change the sign.
Answer: 7/2
4. What slope is parallel to y = 2x + 1?
Show solution
- Parallel lines have the same slope.
Answer: 2
5. What slope is perpendicular to 3/5?
Show solution
- Flip the fraction and change the sign.
Answer: -5/3
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