Line Graphs KS3: Reading and Drawing Graphs of Change

When is a line graph the right choice?

Use a line graph when your data shows change over time — for example, temperature recorded every hour, a person's height measured each year, or monthly rainfall. The x-axis represents time and the y-axis represents the quantity being measured.

A line graph is not appropriate when the x-axis represents categories with no natural order (e.g. different subjects) — use a bar chart instead.

How do you draw a line graph?

Method at a glance:

1. Draw and label the axes. The x-axis shows time; the y-axis shows the measured quantity. Both axes need a unit label (e.g. "Time (months)", "Temperature (°C)").
2. Choose a suitable scale. The scale must go from 0 (or just below the lowest value) to above the highest value. Use an even scale that is easy to read: multiples of 1, 2, 5, or 10 work well.
3. Plot each data point. For each time–value pair, place a small cross (×) or dot at the correct position.
4. Join the points in order. Connect consecutive points with straight lines using a ruler. Do not skip points.
5. Give the graph a title. A clear title such as "Temperature in a garden each hour" makes the graph easy to interpret.

Worked example: drawing a line graph

The table shows the number of books borrowed from a library each month for six months.

• Scale the y-axis from 0 to 160 in steps of 20.
• Plot six points: (Jan, 120), (Feb, 95), (Mar, 110), (Apr, 130), (May, 150), (Jun, 140).
• Join with straight lines left to right.

Reading a value from your graph: To find approximately how many books were borrowed mid-March, read up from "mid-March" on the x-axis to the line, then across to the y-axis. The answer is approximately 120.

How do you describe the trend in a line graph?

A trend is the general direction the graph is moving over time. Use these terms:

• Increasing trend — values generally rise over time.
• Decreasing trend — values generally fall.
• No clear trend — values go up and down with no consistent direction.
• Fluctuating — values rise and fall repeatedly around a roughly constant level.

In the worked example above, the overall trend from January to June is increasing, even though February shows a dip. When describing a trend, comment on the overall pattern first, then mention any exceptions.

How do you read values between plotted points?

This is called interpolation — reading a value from inside the plotted range. Find the time on the x-axis, draw a vertical line up to the graph, then read across horizontally to the y-axis.

Example: The graph shows population at years 2000, 2005, 2010, 2015. To estimate the population in 2007, locate 2007 on the x-axis (two fifths of the way between 2005 and 2010) and read off the corresponding y-value from the line.

Extrapolation — estimating beyond the plotted range — is less reliable. Always state that a value is an estimate when you extrapolate.

What common mistakes should you avoid?

Frequently asked questions

Should the line graph always start at (0, 0)?

No. The time axis begins at the first time point in your data, not necessarily zero. The y-axis should start at or below the lowest value. If the values are all between 80 and 160, you may start the y-axis at 80 and use a scale break (a zig-zag mark near the origin) to show it does not begin at zero.

Can a line graph have more than one line?

Yes — a comparative line graph has two or more lines on the same diagram, using different colours or styles. Each line represents a different group (e.g. boys and girls, two different months). Label each line clearly with a key (legend).

What is the difference between a line graph and a distance–time graph?

Both are line graphs, but a distance–time graph has distance on the y-axis and time on the x-axis, with a specific additional interpretation: the gradient of the line equals the speed. An ordinary line graph does not use gradient to represent speed.

How precise should my plotted points be?

Plot to the nearest half small square on the grid. If your scale has 2 mm squares and each square represents 10 units, plot to the nearest 5 units. Examine the question to see whether your answer is expected to be exact or approximate.

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Professor Pi walks you through data and graphs step by step — add the AI Tutors connector at aitutors.me.