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Conversion graphs

Tutor: Toby

# Conversion graphs

## ​​In a nutshell

Conversion graphs are a tool to convert between units, like between measurements for example. To read them, you just need to know how to read a straight line graph.

## Converting using a graph

#### ​​procedure

 1. Given a conversion graph that converts between unit X on the $x$-axis and unit Y on the $y$-axis, decide whether you want to convert from X to Y or Y to X.​ 2a. If converting from X to Y, read the X value off the $x$-axis and find the corresponding $y$-coordinate on the graph. This is the Y value converted from the X value.​ 2b. If converting from Y to X, read the Y value off the  $y$-axis and find the corresponding $x$-coordinate on the graph. This is the X value converted from the Y value. ​

## Converting currencies

An example of a conversion graph is given below. It shows the relationship between two currencies, pounds sterling and euros.

##### Example 1

Use the graph below to convert $£30$ into euros.

You are converting from pounds to euros. Since pounds is on the $x$-axis, go from $x=30$ up to the line, then across to read the in-line value on the $y$-axis. This is approximately $y=35$. Hence

$£30$​ is approximately $\underline{€35}$

##### Example 2

Use the same currency conversion graph to convert $€50$ into pounds sterling.

To convert from euros to pounds, start on the $y$-axis, and find the corresponding $x$-coordinate. Start at $y=50$ on the $y$-axis, go across until you meet the line, then go down to see the value on the $x$-axis that is in-line.

This is approximately $42$, so

$€50$ is about $\underline{£42}$

Note: The word "approximately" is used because the exact point is not labelled on the axis, so it can be tricky to read the exact value.

## Converting distances

Converting distances on a conversion graph works in the exact same way as converting currencies.

##### Example 3

The graph below shows conversions between miles and kilometres:

Find how many kilometres there are in five miles.

Go to five on the miles axis (the $y$-axis) and trace across until you meet the straight line graph. Then trace down to the kilometres axis (the $x$-axis). It reads approximately $8$, so you have found that five miles is about eight kilometres.

The gradient of the straight line in a conversion graph represents how to convert one of the $x$-unit into $y$-units. Namely, if the gradient is $m$​, then one of the $x$-unit is $m$ of the $y$-units.​

## FAQs - Frequently Asked Questions

### What are conversion graphs?

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