Line graph

A line graph is a chart that shows how something changes, usually over time. Each data value is plotted as a point, and the points are joined with straight line segments, so you can see at a glance whether the values are going up, going down or staying the same. Time goes along the horizontal x-axis and the quantity you measured goes up the vertical y-axis.

What is a line graph?

Say you record the temperature in your town every two hours on a spring day:

The table holds the numbers, but the pattern is hard to see. Plot each pair as a point and join the points in order, and the shape of the day appears:

Here x is the time of day on a 24-hour clock, so 14 means 2 pm, and y is the temperature in °F. The line climbs all morning, peaks at 2 pm and falls in the evening.

Parts of a line graph

How to read a line graph

1. Read the title and axis labels so you know what is being measured and in what units.
2. Check the scale on each axis. Each grid line might stand for 1, 2, 5 or 10 units.
3. To find a value, start at the time on the x-axis, move straight up until you hit the line, then read across to the y-axis.
4. To see the trend, follow the line from left to right: uphill means increasing, downhill means decreasing, flat means no change.
5. To compare changes, look at steepness. The steepest part of the line is where the value changed fastest.

Example 1: reading the temperature graph

• When was it warmest? At 2 pm, the highest point, at 70°F.
• When did it warm up fastest? Between 8 am and 10 am, the steepest climb: 61 − 54 = 7°F in two hours.
• When did it cool fastest? Between 4 pm and 6 pm: 66 − 58 = 8°F drop.
• What was the change from 6 am to 2 pm? 70 − 48 = 22°F over 8 hours, an average of 22 ÷ 8 = 2.75°F per hour.

Reading between the points

Nobody measured the temperature at 11 am, but the line gives an estimate. 11 am is halfway between 10 am (61°F) and noon (67°F), so the line is halfway between them: about 64°F. Estimating between known points like this is called interpolation. It only works when the quantity changes smoothly. Guessing beyond the last point, called extrapolation, is much less reliable.

Reading a graph and spotting where it rises and falls is the same skill for any graph. Try this question from the Graphing Functions course.

How to make a line graph

1. Put time on the x-axis and the measured quantity on the y-axis.
2. Choose a scale for each axis that fits all your data and uses evenly spaced steps. Look at the smallest and largest values first.
3. Label both axes with names and units, and give the graph a title.
4. Plot each data point carefully: across to the time, up to the value.
5. Join the points in order with straight lines, from left to right. Use a ruler.
6. For more than one set of data, use a different color or line style for each and add a key.

Double line graphs

A double line graph puts two sets of data on the same axes, so you can compare them. For example, the average monthly high temperature in two cities, or the sales of two products, each with its own line. Where the lines cross, the two values are equal. Where they are far apart, the difference is large. Always include a key.

Line graph vs bar graph

Use a line graph when the order of the x values matters and it makes sense to join them, like hours or years. Use a bar graph when the categories are separate and could go in any order: joining "apples" to "bananas" with a line would mean nothing.

Line graph vs line plot vs scatter plot

• A line plot is not a line graph. It is a number line with an X or dot above each value to show how often it occurs. US students meet line plots from grade 2.
• A scatter plot shows pairs of values as unconnected points to look for a relationship, often with a line of best fit drawn through them. The Linear Regression calculator finds that line.
• A line graph connects its points in order, because each one follows on from the last.

A "line graph" can also mean the graph of a linear equation, a straight line such as y = 2x + 1. That is a different topic: see graphing linear functions.

Check your reading of the temperature graph.

Misleading line graphs

The same data can look dramatic or dull depending on the scale. If the y-axis starts at 47 instead of 0, a change from 48 to 70 fills the whole graph and looks enormous. That is fine for showing detail, but a graph meant to compare sizes should make it clear when the axis does not start at 0. Uneven time gaps on the x-axis also distort the shape, so check that the time steps are equal.

Common mistakes

• Uneven scales. Each step on an axis must stand for the same amount.
• Putting time on the y-axis. Time almost always goes along the bottom.
• Missing labels or units. A graph without them can't be read.
• Joining points out of order, or joining points that are separate categories.
• Reading the wrong scale in a double line graph with two y-axes.
• Trusting extrapolation. A line that rose all morning will not rise forever.

Practice with a short timed paper

Reading graphs and data displays comes up on math tests at every level. The daily Pre-Algebra & Algebra 1 and Geometry, Algebra 2 & SAT Math papers are short timed practice tests of 8 questions, with a new one every day.

Read next

Maths · StatisticsBar graph: what it is, how to draw and read oneWhat a bar graph is, its types, how to draw and read one step by step, and how a bar graph differs from a histogram, with worked examples.