This deep dive covers Worked Examples 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 7 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 7 of 10
Practice
14 questions
Recall
12 flashcards
Worked Examples
Example 1: Parallel Line
Find the equation of the line parallel to y = 3x - 2 that passes through (1, 5).
Solution:
- Original gradient: m = 3
- Parallel line has same gradient: m = 3
- Using point (1, 5): 5 = 3(1) + c
- So c = 2
- Equation: y = 3x + 2
Example 2: Perpendicular Line
Find the equation of the line perpendicular to y = -2x + 7 that passes through (4, -1).
Solution:
- Original gradient: m₁ = -2
- Perpendicular gradient: m₂ = -1/(-2) = 1/2
- Using point (4, -1): -1 = (1/2)(4) + c
- So: -1 = 2 + c, therefore c = -3
- Equation: y = (1/2)x - 3
Example 3: Checking Perpendicular
Are the lines y = 3x + 1 and y = (-1/3)x + 5 perpendicular?
Solution:
- Gradients: m₁ = 3 and m₂ = -1/3
- Check: m₁ × m₂ = 3 × (-1/3) = -1 ✓
- Yes, they are perpendicular
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.
Practice Questions for Parallel & Perpendicular
Which of the following is true about two parallel straight lines?
Explain why a horizontal line and a vertical line are always perpendicular to each other. Your explanation must refer to gradients.
Quick Recall Flashcards
14 questions on Parallel & Perpendicular — practise free
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