Linear Graphs & Gradients — GCSE Mathematics Revision
Revise Linear Graphs & Gradients for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Quadratic GraphsWhat is Linear Graphs & Gradients?
A linear graph is a straight line with equation y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). The gradient is calculated as rise ÷ run, or (y₂ - y₁) ÷ (x₂ - x₁). Parallel lines have equal gradients. Perpendicular lines have gradients that multiply to give -1.
Step-by-step explanationWorked example
Find the gradient of the line through (2, 3) and (6, 11). Gradient = (11-3)/(6-2) = 8/4 = 2.
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Common mistakes
- 1Mixing up the x and y coordinates when calculating gradient — it is change in y divided by change in x, not the other way round.
- 2Forgetting that a negative gradient means the line slopes downward from left to right.
- 3Not rearranging the equation into y = mx + c form before reading off the gradient and intercept.
- 4For perpendicular lines, just negating the gradient instead of taking the negative reciprocal.
Linear Graphs & Gradients exam questions
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Linear Graphs & Gradients
Core concept
A linear graph is a straight line with equation y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). The gradient is calculated as rise ÷ run, …
Frequently asked questions
How do I find the equation of a line through two points?
Find the gradient m using (y₂-y₁)/(x₂-x₁). Then substitute one point into y = mx + c to find c. Or use y - y₁ = m(x - x₁).
What is the gradient of a perpendicular line?
The negative reciprocal. If one line has gradient m, the perpendicular line has gradient -1/m. For example, if m = 2, the perpendicular gradient is -1/2.