- 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

- 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

- In this example, we are converting from °F, which is on the
- 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

- 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

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.**

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