Line Graphs and Conversion Graphs
A line graph plots points joined by straight lines to show how a quantity changes, often over time, such as temperature during a day. A conversion graph is a special straight-line graph used to convert between two related quantities, such as pounds and euros or miles and kilometres, without recalculating each time. 11+ papers test reading exact and in-between values from both kinds of graph, describing trends, and using a conversion graph's scale factor to convert values.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the labels and scale on both axes carefully before taking any readings, checking what each gridline represents.
- To read a value from a line graph, find the given point on one axis, trace across or up to the line, then read off the other axis.
- For values between plotted points, estimate by judging the position proportionally along the gridlines.
- For a conversion graph, use one known conversion pair, such as a point where the line crosses a labelled gridline, to work out the scale factor between the two quantities.
- To describe a trend, use phrases such as 'increased steadily', 'decreased then levelled off', or 'stayed constant', referring to specific sections of the graph.
- Where a second point is given, check your conversion works for that point too, to confirm the scale factor is correct.
Worked example
A conversion graph shows pounds (GBP) on the horizontal axis and euros (EUR) on the vertical axis. The graph passes through the origin and shows that 20 pounds converts to 24 euros. Use the graph's scale factor to work out how many euros 55 pounds would convert to.
- Find the scale factor from the given point: 24 euros / 20 pounds = 1.2 euros per pound.
- Multiply the new amount of pounds by this scale factor: 55 x 1.2.
- Calculate: 55 x 1.2 = 55 x 1 + 55 x 0.2 = 55 + 11 = 66.
- 55 pounds converts to 66 euros.
Practice questions
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Q1A line graph shows a plant's height was 12 cm on day 0 and 20 cm on day 4, growing at a steady rate. What was its height on day 2?Show answer
Answer: 16 cm (the plant grows 8 cm over 4 days, or 2 cm per day, so day 2 is 12 + 4 = 16 cm)
Q2A conversion graph shows that 10 miles is equal to 16 km. How many km is 5 miles?Show answer
Answer: 8 km
Q3Using the same conversion graph (10 miles = 16 km), how many miles is 32 km?Show answer
Answer: 20 miles
Q4A temperature line graph shows the temperature rose from 4 degrees C at 6am to 18 degrees C at 2pm, then fell to 10 degrees C by 6pm. Describe, in one sentence, how the temperature changed over the whole day.Show answer
Answer: It rose steadily from 6am to 2pm, then fell from 2pm to 6pm.
Q5A litres-to-gallons conversion graph shows 45 litres is equal to 10 gallons. How many litres is 1 gallon?Show answer
Answer: 4.5 litres
Q6A car's fuel gauge line graph shows the tank was full (50 litres) at the start of a journey and empty after travelling 400 km. Assuming fuel is used at a constant rate, how much fuel is left after 240 km?Show answer
Answer: 20 litres (240 / 400 of the tank has been used, which is 30 litres, leaving 50 - 30 = 20 litres)
Q7True or False: on a conversion graph that passes through the origin, doubling the value on one axis always doubles the corresponding value on the other axis.Show answer
Answer: True
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A line graph shows the number of visitors to a museum each hour. At 10am there were 40 visitors, at 12pm there were 100 visitors, and at 2pm there were 70 visitors. (a) By how many did the number of visitors change between 10am and 12pm? (b) Describe what happened to the number of visitors between 12pm and 2pm.
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A conversion graph for pounds (GBP) to US dollars (USD) shows that 8 pounds converts to 10 dollars. (a) Work out the scale factor to convert pounds to dollars. (b) A tourist wants to buy a souvenir costing 45 dollars. Using your scale factor, work out how many pounds this costs.
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Free printable worksheet
Want more practice on paper? Download the line graphs and conversion graphs worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 24 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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