Lines in the Real World

Part of Linear Graphs Problems · Section 1 of 10

IntroductionUnit: GraphsGCSE

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. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. 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.

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.

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

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