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GCSE Linear Graphs Revision Guide
Master everything from basic gradients to complex perpendicular line equations for your GCSE Mathematics examinations.
Foundation
Higher Tier
Exam Practice
Formulae
Topic Overview
Linear graphs represent relationships where the rate of change is constant. They form the foundational cornerstone of coordinate geometry, bridging algebraic equations and visual representation on a Cartesian plane.
Quick Navigation
Equation
Gradient
Parallel
Perpendicular
Essential Formulae
Equation of a Straight Line
y=mx+c
Gradient Formula
m = (y₂ - y₁) / (x₂ - x₁)
Parallel Gradient Rule
m₁ = m₂
Lesson Modules
Equation of a line
Learn how to find and use the y = mx + c form to describe any straight line precisely.
Gradient and intercept
Understanding slope (m) and exactly where lines cross the y-axis (c).
Parallel & Perpendicular
Working with related gradients and the perpendicular rule m₁ × m₂ = -1.
Core Subtopics
Structured lessons for every syllabus requirement.
Worked Example
Step-by-Step Walk through
THE QUESTION
Find the equation of the line passing through (2, 5) and (4, 11).
Method
- Find Gradient (m): (11 – 5) / (4 – 2) = 6 / 2 = 3
- Substitute into y = mx + c: 5 = 3(2) + c
- Solve for c: 5 = 6 + c → c = -1
Common Mistake
Do not swap the x and y coordinates when calculating the gradient. Always use (y₂ - y₁) on top.
Final Answer
y = 3x - 1
Revision Resources
Worksheet
Revision Quiz
Exam Qs
Mark Scheme
Playlist
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Frequently Asked Questions
What does 'm' represent in y=mx+c?
‘m’ represents the gradient or slope of the line. It tells you how much the y-value changes for every 1 unit increase in the x-value.
How do you find the y-intercept?
The y-intercept is the point where the line crosses the y-axis. At this point, x = 0. In the equation y=mx+c, the value of ‘c’ is the y-intercept.
Can a gradient be negative?
Yes! A negative gradient means the line slopes downwards from left to right. As x increases, y decreases.
