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
- 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.
a)
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.
Approximately $225
b)
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
c)
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.
