GCSE Mathematics Revision — Linear Graphs & Gradients
Revise Linear Graphs & Gradients for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP.
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- Linear Graphs & Gradients in GCSE Mathematics: explanation, examples, and practice links on this page.
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What 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 examples
Worked example 1: Core method
Find the gradient of the line through (2, 3) and (6, 11). Gradient = (11-3)/(6-2) = 8/4 = 2.
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Linear Graphs & Gradients idea being tested, show the method or evidence, then explain why it answers the command word. This helps GCSE Mathematics students avoid memorising one surface pattern.
Worked example 3: Mark-scheme check
Finish by checking the answer against marks: one point for the correct Linear Graphs & Gradients idea, one for accurate working or evidence, and one for a precise final statement. If any step is vague, rewrite it before moving to timed practice.
Mini lesson for Linear Graphs & Gradients
1. Understand the core idea
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).
Can you explain Linear Graphs & Gradients without copying the notes?
2. Turn it into marks
Find the gradient of the line through (2, 3) and (6, 11). Gradient = (11-3)/(6-2) = 8/4 = 2.
Underline the method, evidence, or command-word move that would earn credit in GCSE Algebra.
3. Fix the likely mark leak
Watch for this mistake: Mixing up the x and y coordinates when calculating gradient — it is change in y divided by change in x, not the other way round.
Write one correction rule before doing another practice question.
Practise this topic
Start with low-focus cards for Linear Graphs & Gradients, then move into full exam-style practice when you want the heavier session.
Mini quiz: Linear Graphs & Gradients
Three quick checks for revision practice. They are original StudyVector prompts, not official exam-board questions.
Question 1
In one GCSE sentence, explain what Linear Graphs & Gradients is testing.
Answer: 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).
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Linear Graphs & Gradients question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Mixing up the x and y coordinates when calculating gradient — it is change in y divided by change in x, not the other way round." What should their next repair task be?
Answer: Do one Linear Graphs & Gradients question and review the mistake type.
Mark focus: Error correction and next-step practice.
Linear Graphs & Gradients flashcards
Core idea
What is the main idea in 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) ÷ (x...
Common mistake
What mistake should you avoid in Linear Graphs & Gradients?
Mixing up the x and y coordinates when calculating gradient — it is change in y divided by change in x, not the other way round.
Practice
What is one useful practice task for Linear Graphs & Gradients?
Answer one Linear Graphs & Gradients question and review the mistake type.
Exam board
How should you use board notes for Linear Graphs & Gradients?
Use your own GCSE specification for exact paper wording and depth.
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
Exam-style questions for Linear Graphs & Gradients with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP specifications.
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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.