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9.5 Real-life Graphs

GCSE Maths Foundation · Edexcel · Chapter 9: Graphs

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: conversion graphs, graphs with a fixed charge, and comparing two linear costs. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Read values both ways from a conversion graph, including values beyond the graph
  • Draw a conversion graph from one fact
  • Interpret the y-intercept and the gradient of a straight-line graph in context
  • Compare two costs using graphs and decide which is better value

Key words

  • Conversion graph: A straight-line graph used to change one unit into another, e.g. pounds into euros.
  • Direct proportion: Two quantities that start at 0 together and increase at the same rate. The graph is a straight line through the origin.
  • Fixed charge: A cost you pay whatever happens, e.g. a call-out fee. It is where the line crosses the vertical axis.
  • Rate: How much one quantity changes for each 1 unit of the other, e.g. £30 per hour. It is the gradient.

Reading a conversion graph

Find the value on one axis, go across (or up) to the line, then read off the other axis. Always check the scale: on this graph each small square is 2 units.

Worked example: reading both ways

Change £30 into euros: up from 30 to the line, then across. €36.
Change €48 into pounds: across from 48 to the line, then down. £40.

Answer: £30 = €36, €48 = £40

Worked example: beyond the graph

Change £200 into euros. The graph only goes to £50.
£200 = 4 × £50, and £50 = €60, so £200 = 4 × €60 = €240.

Answer: €240

Key fact: This only works because the line goes through (0, 0): the two amounts are in direct proportion.

Drawing a conversion graph

You need two points. One is always (0, 0). Get the other from the fact you are given, then join with a ruler.

Worked example: miles and kilometres

5 miles is about 8 km. Draw a graph for 0 to 50 miles.
50 miles = 10 × 5 miles, so 50 miles ≈ 10 × 8 = 80 km.
Plot (0, 0) and (50, 80) and join them. Check: (25, 40) should be on the line.

Answer: a straight line from (0, 0) to (50, 80)

Graphs with a fixed charge

Many costs are a fixed amount plus an amount per unit. The graph is still a straight line, but it does not start at 0.

  • Where the line meets the cost axis (y-intercept); What it means here the fixed charge: £40
  • Gradient (up 30 for every 1 across); What it means here the rate: £30 per hour
  • Line does not pass through (0, 0); What it means here cost is not directly proportional to time

Worked example: working out costs

Cost for 3 hours = 40 + 3 × 30 = £130. Read from the graph to check.
4 hours cost £160, which is not double the 2-hour cost of £100.

Answer: £130

Comparing two plans

When two lines are drawn on the same axes, the lower line is cheaper. Where the lines cross, the two plans cost the same.

Worked example: two taxi firms

For 4 miles: A costs 3 + 4 × 1.5 = £9 and B costs 4 × 2 = £8. B is cheaper.
The lines cross at (6, 12): both firms charge £12 for 6 miles.
For 10 miles: A costs 3 + 15 = £18 and B costs £20. A is cheaper.

Answer: B is cheaper below 6 miles, A is cheaper above 6 miles

Common mistakes

  • Misreading the scale. Work out what one small square is worth before you read a value.
  • Reading from the wrong axis, e.g. answering in pounds when the question asks for euros.
  • Doubling a value from a fixed-charge graph. 4 hours does not cost twice as much as 2 hours when there is a fixed charge.
  • Forgetting the units in the answer (£, €, km, miles).

Revision questions

Try these, then check your answers below each one.

Question 1. A conversion graph between pounds (£) and euros (€) is a straight line through (0, 0) and (50, 60). How many euros is £20 worth?

Answer: 24 €

Working: £1 = €60 ÷ 50 = €1.20, so £20 = 20 × 1.20 = €24.

Question 2. Using the same graph (£50 = €60), how many pounds is €90 worth?

Answer: 75 £

Working: €90 ÷ 1.20 = £75.

Question 3. The graph of the cost of hiring a bike is a straight line from (0, 8) to (4, 20), where x is the time in hours and y is the cost in £. What is the fixed charge? (Choose from: £8, £3, £20, £12.)

Answer: £8

Working: At 0 hours the cost is £8, so the fixed charge is £8.

Related lessons

Continue in the full course

This lesson is section 9.5 (EGCMF0905) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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