Graphing Linear Equations
Plot the intercept then use the slope to find more points.
About this topic
To graph a linear equation, plot at least two points that satisfy it and draw a straight line through them, adding arrows to show it continues. Common methods are a table of values, using the slope and y-intercept, or using the two intercepts.
The graph is the picture of all solutions: every point on the line makes the equation true, and every point off the line makes it false. For y = 2x − 3, choosing x = 0, 1, 2 gives points (0, −3), (1, −1) and (2, 1). A third point is a useful check, because if the three do not line up there is an arithmetic error somewhere.
Linear graphs model steady change: a phone plan, a car moving at constant speed, or a savings account with fixed deposits. Choosing a sensible scale on each axis helps the graph fill the grid and reveals the trend.
Remember to label the axes and the line, and extend it past the points you plotted. A common error is to connect points with a curve or to stop the line at the points. For word problems, the line may only make sense for non-negative values, so you might draw only part of it.
Key ideas
- Start at the y-intercept
- Rise and run to the next point
- Draw a line through all points
Quick check
Use cases: where Graphing Linear Equations helps
- Homework: review the key idea behind Graphing Linear Equations before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Graphing Linear Equations without notes.
- Visual learning: play with the interactive lab to see how Graphing Linear Equations changes when you adjust its inputs.
- Teaching a friend: explain Graphing Linear Equations in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Graphing Linear Equations?
Plot the intercept then use the slope to find more points.
What will I learn in Graphing Linear Equations?
Start at the y-intercept. Rise and run to the next point. Draw a line through all points.
Is Graphing Linear Equations part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Graphing Linear Equations lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Graphing Linear Equations?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.