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Finding Parallel and Perpendicular Lines

Part of Parallel & Perpendicular · GCSE GCSE Mathematics revision

This deep dive covers Finding Parallel and Perpendicular Lines within Parallel & Perpendicular for GCSE Mathematics. Revise Parallel & Perpendicular in Graphs for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 6 of 10

Practice

14 questions

Recall

12 flashcards

Finding Parallel and Perpendicular Lines

To find a parallel line:

  1. Find the gradient of the original line
  2. Use the same gradient for the new line
  3. Use given point to find the y-intercept
  4. Write equation in form y = mx + c

To find a perpendicular line:

  1. Find the gradient of the original line
  2. Calculate the perpendicular gradient: -1/m
  3. Use given point to find the y-intercept
  4. Write equation in form y = mx + c

Special Cases

Original Line Parallel Line Perpendicular Line
Horizontal (m = 0) Also horizontal Vertical (x = constant)
Vertical (undefined m) Also vertical Horizontal (y = constant)
m = 1 m = 1 m = -1
m = 2 m = 2 m = -1/2

Keep building this topic

Read this section alongside the surrounding pages in Parallel & Perpendicular. That gives you the full topic sequence instead of a single isolated revision point.

The Gradient RulesWorked ExamplesTrain Tracks and Right AnglesParallel Lines

Practice Questions for Parallel & Perpendicular

Which of the following is true about two parallel straight lines?

  • A. They have the same gradient but different y-intercepts
  • B. Their gradients multiply to give -1
  • C. They have the same gradient and the same y-intercept
  • D. One gradient is the negative of the other
1 markfoundation

Explain why a horizontal line and a vertical line are always perpendicular to each other. Your explanation must refer to gradients.

2 marksstandard

Quick Recall Flashcards

What is the gradient rule for perpendicular lines?
Perpendicular lines have gradients that multiply to -1. If L1 perp L2 then m1 x m2 = -1.
What is the gradient rule for parallel lines?
Parallel lines have equal gradients. If L1 has gradient m1 and L2 has gradient m2, then L1 || L2 means m1 = m2.

14 questions on Parallel & Perpendicular — practise free

Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.

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The Gradient Rules

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Worked Examples