Conversion Graphs

What is a conversion graph?

A conversion graph is a linear graph which shows the relationship between two quantities
They allow you to convert between the two units or quantities by reading values off the graph at different points on the line
They may be used for

Converting between units of temperature e.g. degrees Celsius (°C) and degrees Fahrenheit (°F)
Converting between currencies e.g. Dollars ($) and Yen (¥)
Converting between units of volume e.g. Litres and Gallons
Calculating a charge based on usage e.g. a taxi driver charging per kilometre driven

How do I use a conversion graph?

Using the below graph, which converts temperatures between Celsius (°C) and Fahrenheit (°F), as an example

cie-igcse-conversion-graphs-f-to-c

Suppose we want to convert 100 °F into °C
Identify the axis you are converting from
- In this example, we are converting from °F, which is on the y-axis
Using a ruler, draw a line from the value you are interested in, towards the graphed line
- In this example, we have drawn a horizontal line from 100 °F
Using a ruler, draw a line from the point of intersection with the graphed line, to the other axis, and read off the result
- In this example, we have shown that 100 °F is equal to around 37.8 °C

Exam Tip

Before reading a value from an axis, determine the scale that is being used
- 1 square on the graph could represent 1, 2, 5, or any other number of units
- The scales on the x and y axes may not be the same

Worked example

The graph below shows the price charged by a plumber for the time spent on a particular job. The y-axis shows the price in dollars, and the x-axis shows the number of hours spent working on the job.

Find the price charged for a job which took 3 hours.

Draw a vertical line from the x-axis at 3 hours, and read off the graph on the y-axis.

cie-igcse-conversion-graphs-we-2

Approximately $225

A particular job cost $320. Find the length of time the job took.

Draw a horizontal line from the y-axis at $320, and read off the graph on the x-axis

Approximately 4.5 hours

The plumber charges a callout fee; a fee charged for travelling to the customer and inspecting the job before starting any work. Find the price of the callout fee.

This would be the price charged for 0 hours; the y-intercept of the graph.
Read this value off the graph at the point where the line graph meets the y axis.

Approximately $45.