Line Graphs — Definition, Formula & Examples
A line graph is a chart that uses points connected by straight lines to show how data changes over time or across ordered categories. Each point sits where a value on the horizontal axis meets a value on the vertical axis.
A line graph is a two-dimensional data display in which individual data values are plotted as points on a coordinate grid—with the independent variable (often time) on the horizontal axis and the dependent variable on the vertical axis—and consecutive points are joined by line segments to emphasize trends and rates of change.
How It Works
To create a line graph, first draw a horizontal axis (x-axis) and a vertical axis (y-axis) and label each one. Choose an even scale for each axis that fits your data. Plot each data pair as a dot where the two values meet on the grid. Finally, connect the dots from left to right with straight lines. The rising and falling line segments make it easy to spot whether values are increasing, decreasing, or staying the same.
Worked Example
Problem: A student recorded the high temperature each day for five days: Monday 60°F, Tuesday 65°F, Wednesday 62°F, Thursday 70°F, Friday 68°F. Create a line graph and identify the day with the biggest temperature jump.
Step 1: Draw the axes. Label the x-axis with the days (Mon–Fri) and the y-axis with temperature in °F. Choose a scale from 55°F to 75°F, counting by 5s.
Step 2: Plot the five points: (Mon, 60), (Tue, 65), (Wed, 62), (Thu, 70), (Fri, 68).
Step 3: Connect the points from left to right with straight line segments.
Step 4: Find each day-to-day change: Mon→Tue = +5, Tue→Wed = −3, Wed→Thu = +8, Thu→Fri = −2. The steepest upward line segment goes from Wednesday to Thursday.
Answer: The biggest temperature jump was an 8°F increase from Wednesday to Thursday, shown by the steepest rising segment on the graph.
Another Example
Problem: A class tracked how many books they read each month: September 12, October 18, November 15, December 24. What trend does the line graph show?
Step 1: Label the x-axis with the months (Sep–Dec) and the y-axis with number of books (scale 0 to 30 by 5s).
Step 2: Plot the points: (Sep, 12), (Oct, 18), (Nov, 15), (Dec, 24) and connect them.
Step 3: Read the line: it rises from Sep to Oct, dips in Nov, then rises sharply to Dec. The overall trend is upward—the class read more books over time, even though November was a slight dip.
Answer: The line graph shows an overall upward trend in books read, with a small decrease in November.
Visualization
Why It Matters
Line graphs appear constantly in science class when you track experiment results over time, and in social studies when you compare population or economic data across years. Understanding how to read and build line graphs is a core skill on state math assessments from third grade onward. Professionals in weather forecasting, medicine, and business rely on line graphs daily to spot trends and make predictions.
Common Mistakes
Mistake: Using uneven spacing on the axes (for example, jumping from 10 to 20 and then from 20 to 50 in the same-sized gap).
Correction: Always use equal intervals on each axis so the line accurately represents changes in the data.
Mistake: Connecting points when the x-axis categories have no meaningful order (such as plotting favorite fruits and drawing lines between them).
Correction: Line graphs require an ordered sequence on the x-axis. For unordered categories, use a bar graph instead.