Conversion Graphs (Edexcel GCSE Maths: Foundation)

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Conversion Graphs

What is a conversion graph?

  • A conversion graph is a straight-line graph relating two quantities
    • You can convert (change) between them by reading values off the graph
  • Common examples include
    • Temperature
      • degrees Celsius (°C) and degrees Fahrenheit (°F)
    • Currency
      • Dollars ($) and Yen (¥)
    • Volume
      • Litres and gallons
    • Prices
      • A taxi driver charging per kilometre driven
  • The gradient of a conversion graph represents the rate of change
    • If the y-axis is the cost of a taxi journey (£) and the x-axis is the distance travelled (mile) then the gradient represents the cost per mile
      • A gradient of 5 means the cost increases by £5 for each mile travelled

How do I use a conversion graph?

  • Find the cost of 20kg using the conversion graph below
    • Start at 20kg on the x-axis
    • Draw a vertical line to the graph
    • Then a horizontal line across to the y-axis
    • Read off the value
      • $12
  • Find how many kilograms can be bought with $30
    • Start at $30 on the y-axis
    • Draw a horizontal line to the graph
    • Then a verical line down to the x-axis
    • Read off the value
      • 50kg
  • You can use proportion to find values that on not on the axes
    • To find the cost of 120kg
      • 120kg = 6 × 20kg costs 6 × $12 = $72
      • 120kg = 50kg + 50kg + 20kg costs $30 + $30 + $12 = $72
    • You can only do this if the graph starts at the origin

conversion-graph

How do I use a conversion graph that does not start at the origin?

  • Convert 100°F into Celsius using the conversion graph below
    • Start at 100°F on the y-axis
    • Draw a horizontal line to the graph
    • Then a vertical line down to the x-axis
    • Read off the value
      • almost equal to37.5°C
      • Answers between 37°C and 38°C would be accepted
      • (The true answer is 37.8°C to 1 decimal place)
  • The graph starts at 32 on the y-axis
    • This means that 0°C is 32°F
    • This starting value sometimes represents a fixed cost when money is involved
      • It could represent the fixed charge for the cost of a taxi fare
  • To convert values that are not on the axis
    • You would need to find an equation for the straight-line

A conversion graph for temperature in degrees Celsius and Fahrenheit

Examiner Tip

  • Always check the scales of the axes!

Worked example

The graph below shows the price (in dollars, $) charged by a plumber for the time spent (in hours) on a particular job.

 

cie-igcse-conversion-graphs-we-1

 

(a)
Estimate the price charged for a job that takes 3 hours.
 

Draw a vertical line up from the x-axis at 3 hours
Then a horizontal line across to the y-axis
Read off the value
 

cie-igcse-conversion-graphs-we-2 

Approximately $225

Answers between $220 and £230 are accepted
 

(b)

A particular job costs $320. Estimate, to the nearest half hour, how long this job took.
  
Draw a horizontal line across from the y-axis at $320
Draw a vertical line down to the x-axis
Read off the value to the nearest 0.5 hours
 

cie-igcse-conversion-graphs-we-3 

4.5 hours (to the nearest half hour)

 

(c)

The plumber charges a fixed callout fee for travelling to the customer and inspecting the job before starting any work.

Find the price of the callout fee.
  

Before starting work means 0 hours of work has been done
Find the price charged for 0 hours
This is the y-intercept of the graph

Approximately $45

Answers between $40 and £50 are accepted

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Mark

Author: Mark

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.