How to Graph a Linear Equation

A linear equation makes a straight line when graphed. Once you understand slope and intercepts, graphing lines becomes much easier.

Quick idea

To graph a line, you need enough information to plot two points or to start at the y-intercept and use the slope.

Steps

1. Rewrite the equation in a form you understand.
2. Find two points that satisfy the equation, or identify the slope and y-intercept.
3. Plot the points on the coordinate plane.
4. Draw a straight line through them.

Worked example

Graph y equals 2x plus 1.

Full solution

Step-by-step walkthrough

Step 1

The y-intercept is 1, so start at (0, 1).

Step 2

The slope is 2, which means rise 2 and run 1.

Step 3

Plot another point at (1, 3), then draw the line.

Common mistake

Do not treat the slope as a single point. Slope tells you how to move from one point to another.

Practice problems

1. Graph y = x + 2.
2. Graph y = -2x + 3.
3. Graph y = 1/2 x - 1.

Answers

1. Start at 2, slope 1.
2. Start at 3, slope -2.
3. Start at -1, slope 1/2.

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• What Is Slope? Rise Over Run Explained
• Slope-Intercept Form Explained
• How to Solve Systems by Elimination