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GCSE Graphs Revision Guide
Master linear, quadratic, and cubic graphs with our comprehensive guide designed for AQA, Edexcel, and OCR specifications.
Foundation
Higher Tier
Exam Practice
Formulae
Topic Overview
Coordinate geometry is a fundamental pillar of GCSE Mathematics. This guide covers the relationship between algebraic equations and their visual representations on a Cartesian plane. You will explore how to plot points, calculate gradients, and understand how transformations—such as reflections, translations, and stretches—affect the parent functions of linear and non-linear graphs.
Whether you are preparing for the Foundation or Higher tier, mastering these concepts is essential for success in higher-level algebra and calculus.
Quick Navigation
Formulae
Lessons
Examples
Resources
Essential Formulae
y = mx + c
m = gradient, c = y-intercept
Straight Line Equation
Gradient Formula
m = Δy / Δx
Change in y divided by change in x
Lesson Modules
Equation of a Line
Mastering y=mx+c for all exam boards.
Distance-Time
Analysing speed from gradients.
Reflections
Mirror lines and coordinates.
Translations
Vector shifts on the plane.
Parallel Lines
Same gradient, different c.
Real-Life Graphs
Conversion and rate graphs.
Plotting
Tables of values & accuracy.
Stretches
Vertical and horizontal scale.
Gradient & Intercept
Finding m and c values.
Core Subtopics
Structured lessons for every syllabus requirement.
Worked Example
Step-by-Step Walkthrough
THE QUESTION
Find the equation of the line that passes through (2, 5) and (4, 9).
Method
- Find gradient (m): (9 – 5) / (4 – 2) = 4 / 2 = 2.
- Substitute m and point (2, 5) into y = mx + c.
- 5 = (2 * 2) + c => 5 = 4 + c.
- Solve for c: c = 1.
Common Mistake
Using (x1 - x2) / (y1 - y2) instead of (y2 - y1) / (x2 - x1). Always remember: "Rise over Run".
Final Answer
y = 2x + 1
Revision Resources
Worksheet
Worksheet (PDF)
Interactive Quiz
Timed interactive y=mx+c quiz.
Exam Questions
Past paper questions by difficulty.
Mark Scheme
Step-by-step solutions for all Qs.
Playlist
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Expert Video Tutorials
Related Topics
Frequently Asked Questions
What is the gradient?
The gradient represents the steepness of a line. In the equation y = mx + c, it is represented by the letter ‘m’. It is calculated by finding the change in y divided by the change in x between two points.
How do I find the y-intercept?
The y-intercept is the point where the line crosses the y-axis (where x = 0). In y = mx + c, it is the constant value ‘c’.
Are transformations on the Higher paper?
Yes, complex transformations of the form y = f(x) + a or y = f(x + a) are predominantly found on the Higher tier paper.
