# 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. S**tart 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

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.