Line Graphs

What a line graph shows

A line graph is a way of showing how one quantity changes in response to another. By far the most common version plots a measurement against time, such as temperature through a day, a plant's height over weeks, or the distance a car has travelled. The points are joined with straight line segments so we can follow the story of the change from left to right.

Line graphs are perfect for continuous data — data that exists at every moment, not just at the instants we happened to measure. Temperature does not jump from one reading to the next; it flows smoothly. Because of that, the line between two plotted points has real meaning, and we can read sensible in-between values. This is what separates a line graph from a bar chart, which compares separate, unconnected categories.

The parts of a line graph

Every well-made line graph has the same features:

• A title stating what the graph is about.
• A horizontal axis (the x-axis), usually showing time, with a label and units.
• A vertical axis (the y-axis), showing the measured quantity, with a label and units.
• A scale on each axis with evenly spaced numbers.
• Plotted points, each marked with a small cross or dot, joined by lines.

Before reading any value, find the scale. The gridlines might go up in 1s, but they might just as easily climb in 2s, 5s, 10s or 50s. Misreading the scale is the single most common error, and it makes every answer wrong. This is exactly the interval-reading skill from Reading Scales and Measuring.

Plotting points

Each point on a line graph is a pair of values: one from the horizontal axis and one from the vertical axis, written (across, up). To plot a point:

1. Start at the origin (where the axes cross).
2. Move across to the first value on the horizontal axis.
3. Move up to the second value on the vertical axis.
4. Mark a neat cross. After plotting every point, join them in order with straight lines.

Worked example 1: plotting a temperature graph

A class records the outdoor temperature each hour:

Time	8:00	9:00	10:00	11:00	12:00
Temperature (°C)	6	9	13	16	18

To plot the 10:00 reading, go across to 10:00 on the time axis, then up to 13 on the temperature axis, and mark a cross. Repeat for every column, then join the crosses. The result is a line that climbs steadily through the morning.

Reading values from a graph

There are two everyday reading tasks.

Reading up: given a time, find the value. Find the time on the horizontal axis, go straight up to the line, then across to the vertical axis to read the value.

Reading across: given a value, find the time. Find the value on the vertical axis, go across to the line, then straight down to read the time.

Worked example 2: reading between the points

Using the graph above, estimate the temperature at 10:30.

1. 10:30 is halfway between the 10:00 point (13°C) and the 11:00 point (16°C).
2. Halfway up between 13 and 16 is 13 + (3 ÷ 2) = 14.5°C.

Because temperature is continuous, this in-between reading is a sensible estimate — exactly why a line graph, not a bar chart, was the right choice.

Describing the trend

The real power of a line graph is showing the trend — the overall direction of change. Describe it using the shape of the line:

Line shape	What it means
Rising (going up)	The quantity is increasing
Falling (going down)	The quantity is decreasing
Flat (horizontal)	The quantity is staying the same
Steep	Change is fast
Gentle	Change is slow

A good description names the trend and points to where it changes. For the temperature graph you might write: "The temperature rose all morning. It rose fastest between 9:00 and 10:00, where the line is steepest, and more slowly after 11:00 as the line flattens."

Steepness means rate of change

The steepness, or gradient, of a line section tells you how fast the quantity is changing, not just whether it is going up or down. Between 9:00 and 10:00 the temperature jumped 4°C in one hour; between 11:00 and 12:00 it rose only 2°C in an hour. The first section is steeper because the change per hour is greater. A steeper line always means a faster rate of change. A perfectly flat section means the rate is zero — nothing is changing.

Worked example 3: a distance–time graph

A cyclist's journey is shown below.

Time (min)	0	10	20	30	40
Distance (km)	0	4	8	8	12

• From 0 to 20 minutes the distance climbs steadily: the cyclist is moving at a constant speed (4 km every 10 minutes).
• From 20 to 30 minutes the line is flat: the distance stays at 8 km, so the cyclist has stopped for a rest.
• From 30 to 40 minutes the line rises again as the cyclist sets off once more.

On a distance–time graph, a flat line does not mean the cyclist is at the start — it means they are not moving. Reading the shape correctly tells the whole story of the journey.

Comparing two lines on one graph

Graphs often show two lines at once so we can compare. Each line needs its own colour or style, explained in a key (legend). Suppose one graph shows the temperature in two cities across a day. You can then ask:

• Which city was warmer at midday? (Read both lines at 12:00 and compare.)
• When were the two cities the same temperature? (Look for where the lines cross.)
• Which city warmed up faster in the morning? (Compare the steepness of the two lines.)

The crossing point is especially useful: it marks the moment two quantities were equal.

Common mistakes to avoid

• Ignoring the scale. Always check what one gridline is worth before reading.
• Plotting (up, across) instead of (across, up). The first number is always horizontal.
• Misreading a flat line. Flat means no change, which on a distance–time graph means stopped, not at the start.
• Using a line graph for the wrong data. If the categories are separate things, like favourite fruits, a line graph is meaningless because there is nothing "between" apples and bananas. Use a bar chart instead.

Why line graphs are so powerful

Why bother converting a table of readings into a line? Because a table tells you the values, but a line graph tells you the story. In one glance you see whether things are rising or falling, where the change is fastest, where something paused, and how two trends compare. Scientists use them to track experiments, doctors to follow a patient, and economists to watch prices. The line turns a column of numbers into a shape your eye can read instantly — and that is information you simply cannot grab from a list. Once you can also summarise data with averages, as in Mean, Median, Mode and Range, you will have a powerful toolkit for handling data.

Activity: build a line graph

Track something that changes over time for one week.

1. Choose a measurement: the daily maximum temperature, the minutes of homework you do, or the height of a fast-growing seed.
2. Each day, record the value in a neat table.
3. Draw axes, choose a sensible scale that fits your largest value, and label both axes with units.
4. Plot each point (day, value) and join them with straight lines. Add a clear title.
5. Write three sentences describing the trend: when did it rise, fall or stay flat, and where was the change fastest?

Summary

A line graph plots a changing quantity against time and joins the points so we can read trends and in-between values. Read the scale first, plot points as (across, up), and describe the line by its direction and steepness. Use line graphs for continuous data and crossing points to compare two sets. With this skill you can read the story behind almost any changing measurement.