IGCSE Equation of a Line: Complete Guide for Cambridge IGCSE Mathematics

IGCSE equation of a line is an essential coordinate geometry topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering y=mx+c form, point-slope form, and finding line equations is essential for solving coordinate geometry problems.

This comprehensive IGCSE equation of a line guide covers everything you need to know, including different forms of line equations, finding equations from points, parallel and perpendicular lines, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to write line equations in different forms, find equations from given information, identify parallel and perpendicular lines, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Equation of a Line Matters

IGCSE equation of a line is an essential coordinate geometry topic. Here’s why it’s so important:

• High frequency topic: Line equation questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for coordinate geometry and graph work
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in modeling and graph analysis
• Problem-solving skills: Develops coordinate geometry understanding

Key insight from examiners: Students often confuse different forms or make errors finding the y-intercept. This guide will help you master these systematically.

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Understanding Equation of a Line

A line equation describes all points on a straight line.

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Standard Form: y = mx + c

y = mx + c

• m = gradient (slope)
• c = y-intercept

Example 1: Find the equation of a line with gradient 3 and y-intercept -2.

Solution: y = 3x - 2

Answer: y = 3x - 2

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Finding Equation from Two Points

Step 1: Find gradient using m = (y₂ - y₁)/(x₂ - x₁) Step 2: Substitute one point and gradient into y = mx + c to find c

Example 2: Find the equation of the line through A(2, 3) and B(5, 9)

Solution: Gradient: m = (9 - 3)/(5 - 2) = 6/3 = 2 Using point A: 3 = 2(2) + c 3 = 4 + c, so c = -1 Equation: y = 2x - 1

Answer: y = 2x - 1

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Finding Equation from Gradient and One Point

Example 3: Find the equation of a line with gradient -2 passing through (3, 5)

Solution: y = mx + c 5 = -2(3) + c 5 = -6 + c, so c = 11 Equation: y = -2x + 11

Answer: y = -2x + 11

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Parallel Lines

Parallel lines have the same gradient.

Example 4: Find the equation of a line parallel to y = 3x + 1 passing through (2, 5)

Solution: Gradient: m = 3 (same as given line) 5 = 3(2) + c 5 = 6 + c, so c = -1 Equation: y = 3x - 1

Answer: y = 3x - 1

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Perpendicular Lines

Perpendicular lines have gradients that multiply to -1.

Example 5: Find the equation of a line perpendicular to y = 2x + 3 passing through (1, 4)

Solution: Given gradient: m₁ = 2 Perpendicular gradient: m₂ = -1/2 (since 2 × -1/2 = -1) 4 = -1/2(1) + c 4 = -0.5 + c, so c = 4.5 Equation: y = -0.5x + 4.5

Answer: y = -0.5x + 4.5 or y = -x/2 + 9/2

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Common Examiner Traps

• Gradient errors - Use correct formula: (y₂ - y₁)/(x₂ - x₁)
• Y-intercept errors - Substitute correctly to find c
• Parallel/perpendicular confusion - Parallel: same gradient; Perpendicular: gradients multiply to -1

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Practice Questions

Question 1

Find the equation of the line through (1, 2) and (4, 8)

Solution: Gradient: m = (8 - 2)/(4 - 1) = 2 2 = 2(1) + c, so c = 0 Equation: y = 2x

Answer: y = 2x

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📞 Ready to turn shaky line equation skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

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Frequently Asked Questions About IGCSE Equation of a Line

What is the standard form of a line equation?

Standard form: y = mx + c where m is the gradient and c is the y-intercept.

How do I find the equation from two points?

Find the gradient, then substitute one point to find the y-intercept.

How do I find parallel lines?

Parallel lines have the same gradient. Use the same gradient with the new point.

How do I find perpendicular lines?

Perpendicular lines have gradients that multiply to -1. If m₁ = a, then m₂ = -1/a.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Distance, Midpoint and Gradient: Complete Guide - Master coordinate geometry formulas
• IGCSE Linear Equations: Complete Guide - Master solving linear equations
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Equation of a Line with Tutopiya

Ready to excel in IGCSE equation of a line? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
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Book a free IGCSE maths trial lesson and get personalized support to master equation of a line and achieve your target grade.

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