Conversion graphs

A conversion graph is used to change one unit into another. This could be changing between miles and kilometres, pounds to a foreign currency, or the cost of a journey based on the number of miles travelled.

Example 1

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Image caption,
Conversion graph between francs and pounds
Before France joined the Eurozone, their currency was French francs. One British pound was worth approximately 10 francs. Using this, we can draw a conversion graph between pounds and francs.
Image caption,
Conversion graph between francs and pounds
We need three points to plot: £0 = 0 francs, £1 = 10 francs, and £2 = 20 francs.
Image caption,
Conversion graph between francs and pounds
Draw a line through these points and extend it so that it covers the whole graph.
Image caption,
Conversion graph between francs and pounds
To convert £3 into francs, start at 3 on the horizontal axis, as this is where pounds are written and go up vertically until you reach the line.
Image caption,
Conversion graph between francs and pounds
From the line, read horizontally until you get to the axis showing francs. We can now see that £3 = 30 francs.
Image caption,
Conversion graph between francs and pounds
To convert 50 francs into pounds, start at 50 on the axis showing francs and trace horizontally until you hit the line.
Image caption,
Conversion graph between francs and pounds
Now trace vertically to see that 50 francs = £5.
Image caption,
Conversion graph between francs and pounds
If we want to convert a value that is not shown by the graph, eg £8, we will need to use another value to help us. By first finding that £4 = 40 francs, we can double this to find that £8 = 80 francs.

Be careful, as this method will only work if the graph passes through the point (\({0} \text{,} {~0}\)).

Example 2

Tony’s Taxis calculate the cost of a journey using the following conversion graph.

A straight line graph labelled 'Taxi fare calculator'. The y axis is labelled 'cost', and the x axis is labelled 'miles'. A red line rises diagonally from point 2 on the y axis

As you can see from the graph, 0 miles = £2. This is a flat rate added to any journey regardless of the distance travelled.

Question

How much would a journey of 7 miles cost?

If a journey cost £8, how many miles would you expect to have travelled?

You should show your answer on the graph.

As the graph doesn’t pass through (\({0} \text{,} {~0}\)) to undertake a conversion that is outside the scale on the graph a different approach must be taken.

It may be possible to extend the graph further.

A straight line graph labelled 'Taxi fare calculator'. The y axis is labelled 'cost', and the x axis is labelled 'miles'. The x axis has been extended from 12 to 20 miles

We can see from this extended graph that £10 would be the charge for a journey that is 16 miles long.

If it is not possible to extend the graph, we will need to undertake some calculations.

Question

Calculate the cost of a 30 mile journey.

Question

Calculate the distance travelled when the journey costs £15.

Graphs - WJECConversion graphs