IGCSE Maths / Travel and other graphs
Conversion graphs and reading information from graphs
Edexcel International GCSE Maths (4MA1), chapter 10: Travel and other graphs, specification point 3.3f-f. Free lesson.
Read the revision notes · IGCSE Maths past papers
Conversion graphs show how one unit relates to another, so you can read a converted value from the graph. Readings are estimates, and if a value lies beyond the graph, you can use the rate shown by the line.
How to read a conversion graph
Start on the axis with the units of the value you have. Travel to the line, then turn and travel to the other axis. The value you read there is the converted amount. Draw both construction lines because they can earn a mark. For a conversion from miles to kilometres, start on the miles axis and finish on the kilometres axis. For the reverse conversion, start on the kilometres axis and finish on the miles axis.
Read in either direction
The same line works for both directions. The axis you start from depends on the units you are given, and the axis you finish on gives the units of your answer. 50 miles is about 80 km. 32 km is about 20 miles.
When the value is beyond the graph
If the graph does not extend to the value you need, use a pair of values that the graph does show to find the conversion rate. Then multiply by that rate to find the converted amount. The graph shows 50 miles as 80 km, so 80 ÷ 50 = 1.6 km per mile. Use this rate to convert 200 miles: 200 × 1.6 = 320 km.
Check the axis and the accuracy
A graph reading is an estimate because you judge a position against the scale by eye. A reading within half a small square is usually accepted, so do not give more decimal places than the graph can support. For 50 miles, read from the miles axis. Starting from 50 on the kilometres axis converts the wrong quantity. About 80 km is a sensible reading. Writing 80.37 km suggests more accuracy than the graph provides.
Use the scale to estimate another value
You can use the relationship between values to make a quick estimate. Since 12.5 is one quarter of 50, its converted value is about one quarter of 80. 12.5 miles is about 20 km.