Parallel and Perpendicular Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Parallel and Perpendicular.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Parallel lines never intersect and have matching direction; perpendicular lines intersect at right angles.
Parallel tracks run side by side; perpendicular streets form a plus sign.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Direction determines whether lines are parallel or perpendicular.
Common stuck point: Students often confuse 'not parallel' with 'perpendicular'—lines can be neither parallel nor perpendicular.
Sense of Study hint: Check angle or slope evidence rather than relying only on the drawing.
Worked Examples
Example 1
easySolution
- 1 Parallel lines have equal slopes. The slope of y = 2x + 5 is m = 2, so the new line also has m = 2.
- 2 Use point-slope form: y - (-1) = 2(x - 3).
- 3 Simplify: y + 1 = 2x - 6, so y = 2x - 7.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.