GraphsTopic Summary

Knowledge Organiser: Linear Graphs Problems

Part of Linear Graphs Problems · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Linear Graphs Problems within Linear Graphs Problems for GCSE Mathematics. Revise Linear Graphs Problems in Graphs for GCSE Mathematics with 16 exam-style questions and 11 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 10 of 10

Practice

16 questions

Recall

11 flashcards

Knowledge Organiser: Linear Graphs Problems

Key Formula

y = mx + c
m = (y₂ − y₁) ÷ (x₂ − x₁)
Gradient = rate of change
y-intercept = starting/fixed value

Finding the Equation

From graph: read c, calculate m from two points
From two points: calculate m first, then substitute to find c
Always verify by checking both original points
Simultaneous equations: find crossing point of two lines

Key Vocabulary

Gradient: rate of change (rise ÷ run)
y-intercept: starting value (fixed charge)
Simultaneous: two equations solved at the same time
Interpolation: predicting within the data range
Extrapolation: predicting outside the data range

Common Errors

Confusing y-intercept (crosses y-axis) with x-intercept
Not including units with gradient in context questions
Assuming extrapolation is reliable
Not checking final equation against original points

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Keep building this topic

Read this section alongside the surrounding pages in Linear Graphs Problems. That gives you the full topic sequence instead of a single isolated revision point.

Common Misconceptions Lines in the Real World The Equation y = mx + c — Quick Reference

Practice Questions for Linear Graphs Problems

A taxi company charges a fixed fee plus an amount per mile. On a cost graph (£ against miles), what does the y-intercept represent?

A. The cost per mile
B. The total cost of the journey
C. The fixed charge before any miles are travelled
D. The gradient of the line

1 markfoundation

A plumber charges according to the formula C = 40t + 30, where C is the total cost in pounds and t is the time in hours. Explain what the values 40 and 30 represent in this context.

2 marksstandard

Quick Recall Flashcards

Steps to find the equation of a line from a graph

1. Read the y-intercept (c) where line crosses y-axis 2. Choose two clear points on the line 3. Calculate gradient m = (y2 - y1)/(x2 - x1) 4. Write y = mx + c Example: crosses (0, 1), gradient 2 → y = 2x + 1

What does each letter in y = mx + c represent?

y = mx + c m = gradient (steepness of the line) c = y-intercept (where the line crosses the y-axis) Example: y = 3x + 2 has gradient 3 and crosses y-axis at (0, 2).

16 questions on Linear Graphs Problems — practise free

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Common Misconceptions

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Linear Graphs Problems