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Lines in the Real World

Part of Linear Graphs Problems — GCSE Mathematics

This introduction covers Lines in the Real World 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 1 of 10 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 10

Practice

16 questions

Recall

11 flashcards

Lines in the Real World

A plumber charges a £30 call-out fee plus £25 per hour. How do you work out any bill at a glance? Draw a straight-line graph. The y-intercept is £30 and the gradient is £25/hour. Read off the cost for any number of hours in seconds. Straight-line graphs are the most powerful modelling tool at GCSE — master them and you can answer virtually any contextual question the examiner sets.

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.

The Equation y = mx + c — Quick ReferenceFinding the Equation of a LineSolving Simultaneous Equations Graphically

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

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).
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

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The Equation y = mx + c — Quick Reference