Parallel and Perpendicular Lines
Parallel lines share slope; perpendicular slopes are negative reciprocals.
Key idea
Parallel lines share slope; perpendicular slopes are negative reciprocals.
In depth
Parallel lines never meet, so they have equal slopes. Perpendicular lines meet at 90°, and their slopes are negative reciprocals, so m₁m₂ = −1. Rotating a direction by 90° swaps and negates run and rise.
Worked example
A line perpendicular to y = 2x + 1 has slope −1/2.
Formula
Real-world uses
- Designing square corners in construction
- Checking road or railway alignments
Common mistake
Using just the negative or just the reciprocal. You need both.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Parallel and Perpendicular Lines?
Parallel lines share slope; perpendicular slopes are negative reciprocals. It is a topic at the intermediate level in Algebra.
What is the formula for Parallel and Perpendicular Lines?
The key formula is m₁m₂ = −1.
Where is Parallel and Perpendicular Lines used in real life?
Real-world examples: Designing square corners in construction; Checking road or railway alignments.
What should I learn before Parallel and Perpendicular Lines?
Make sure you are comfortable with Standard Form of a Line, the previous topic in Algebra.
What is a common mistake with Parallel and Perpendicular Lines?
Using just the negative or just the reciprocal. You need both.
How can I practise Parallel and Perpendicular Lines?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Parallel and Perpendicular Lines?
Move on to Graphing Linear Equations next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.