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.
Conversion graph between francs and pounds
Be careful, as this method will only work if the graph passes through the point ( ).
Tony’s Taxis calculate the cost of a journey using the following conversion graph.
As you can see from the graph, 0 miles = £2. This is a flat rate added to any journey regardless of the distance travelled.
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
As the graph doesn’t pass through ( ) 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.
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.
Calculate the cost of a 30 mile journey.
Calculate the distance travelled when the journey costs £15.
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.