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

A conversion graph. The y axis, 'Francs', is labelled from 0 to 50, the x axis, 'British pounds', is labelled from 0 to 6

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.

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.

7 miles = £5.50

£8 = 12 miles

A straight line graph labelled 'Taxi fare calculator'. A red line rises diagonally from point 2 on the y axis. 7 miles = £5.50 and £8 = 12 miles are marked 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.

£17.

  1. We know that a 0 mile journey costs £2
  2. We know that a 10 mile journey costs £7
  3. So each 10 miles travelled costs £7 - £2 = £5
  4. 30 miles = 10 miles × 3, so the cost of 30 miles = £5 × 3 = £15
  5. Add on the flat charge of £2 for each journey: £15 + £2 = £17
Question

Calculate the distance travelled when the journey costs £15.

26 miles.

From the graph we can see that £2 = 0 miles and £3 = 2 miles.

This means that after the flat rate of £2, £1 is added on for every 2 miles.

For a journey costing £15, we can subtract the flat rate of £2 to see that £13 has been added on for distance travelled.

As each £1 accounts for 2 miles: 13 × 2 = 26 miles.