GCSE Maths • Foundation & Higher
GCSE Linear Graphs Revision Guide
Understand y = mx + c, calculate gradients, identify intercepts, find equations of straight lines, and solve parallel and perpendicular line problems.
Foundation
Exam practice
Worked examples
What You'll Learn
Recognise y = mx + c
Identify the gradient m and y-intercept c from a straight-line equation.
Calculate gradient
Use rise ÷ run or the coordinates of two points in a consistent order.
Find an equation
Use a gradient and a point to determine the complete equation of a line.
Draw linear graphs
Create a table of values or use the intercept and gradient to plot accurately.
Compare lines
Use gradients to identify parallel and perpendicular relationships.
Key Rules and Formulas
Linear Graph Lessons
Equation of a Line
Move between equations, coordinate tables and straight-line graphs, and find an equation from points or graphical information.
Gradient and Intercept
Interpret m and c, calculate gradients from coordinates, and connect gradient with rate of change.
Parallel and Perpendicular Lines
Compare gradients and find equations of related lines passing through specified points.
CORE SUBTOPICS
Equation of a Line
In y = mx + c, the coefficient of x is the gradient and the constant is the y-intercept. Rearrange an equation into this form before reading m and c.
Gradient and Intercept
Gradient measures the change in y for each unit change in x. A positive gradient rises from left to right; a negative gradient falls; zero gives a horizontal line.
Parallel and Perpendicular Lines
Parallel non-vertical lines have the same gradient. Different y-intercepts make them distinct parallel lines.
Worked Example
Identify gradient and intercept
QUESTION
State the gradient and y-intercept of y = −2x + 7.
- 1. Compare with y = mx + c.
- 2. The coefficient of x is −2, so m = −2.
- 3. The constant is 7, so the y-intercept is (0, 7).
- Answer Gradient = −2; y-intercept = (0, 7).
- Common GCSE Mistakes
- Identify what is given: an equation, graph, gradient, intercept or points.
- Rearrange into y = mx + c if possible.
- Calculate or identify the gradient, keeping signs and point order consistent.
- Use a known point to find c when the full equation is required.
- Apply the equal-gradient or negative-reciprocal rule for related lines.
- Check the result using the original point or a second coordinate.
- Exam Tips
- Calling c the x-intercept instead of the y-intercept.
- Ignoring a negative gradient.
- Calculating change in x ÷ change in y.
- Changing the point order in only one part of the gradient fraction.
- Reading m and c before rearranging the equation into y = mx + c.
- Assuming parallel lines need the same intercept.
- Changing only the sign, but not taking the reciprocal, for a perpendicular gradient.
Ready to Practice?
Printable Worksheet
Practise simplifying, unit conversions, sharing totals, recipe scaling, combined ratios and best-buy comparisons.
Interactive Quiz
Check ratio order, equivalent ratios, total parts, unit prices and common misconceptions.
Exam-Style Questions
Apply ratio methods to money, measures, recipes, maps and multi-stage GCSE contexts.
Watch the Linear Graph Tutorial
A clear walkthrough of y = mx + c, gradients from coordinates, equations through points, and parallel and perpendicular lines.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
m is the gradient, showing the change in y per unit change in x. c is the y-value when x = 0, so the y-intercept is (0, c).
Use (y₂ − y₁)/(x₂ − x₁), subtracting coordinates in the same order. The denominator must not be zero.
Substitute the gradient and point into y = mx + c and solve for c, or use y − y₁ = m(x − x₁) and simplify.
Distinct non-vertical lines are parallel when their gradients are equal. Their intercepts are different.
