Conversion Graphs (Edexcel IGCSE Maths)

Spec point — 3.3F

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 pounds (£)

  • 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 vertical 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

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

    • $\approx$37.5°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

Exam Hint Always double-check the scales of the axes!

Worked Example The graph below shows the price (in pounds, £) charged by a plumber for the time spent (in hours) on a particular job.

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

Answer:

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

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.

Answer:

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

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.

Answer:

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

Final answer: Approximately £45

Final answer: Answers between £40 and £50 are accepted