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Graphing a Linear Equation


There are several methods to graph a linear equation.
In these lessons, we will learn

  • how to graph linear equations by plotting points.
  • how to graph linear equations by finding the x-intercept and y-intercept.
  • how to graph linear equations using the slope and y-intercept.

Related Topics:
More Algebra Lessons

More Geometry Lessons

Algebra Worksheets

Algebra Games

Graph Linear Equations by Plotting Points

It only takes 2 points to draw a graph of a straight line. In other words, if we can find two points that satisfies the equation of the line, then the line can be accurately drawn.

Example :

Draw the line with equation y = 2x – 3

Solution :

Try to choose values that will give whole numbers to make it easier to plot.

Step 1 : Let x = 0

y = 2(0) – 3
y = – 3

Step 2 : Let x = 2

y = 2(2) – 3
y = 1

Step 3 : Plot the two points on the Cartesian plane

Step 4 : Draw a straight line passing through the two points

This video shows how to use a t-table to graph linear equations.

This following video shows how to graph a linear equation by plotting points.

Graph Linear Equations by using X and Y Intercepts

The x-intercept is where the line crosses the x-axis. At this point, the y-coordinate is 0.
The y-intercept is where the line crosses the y-axis. At this point, the x-coordinate is 0.

When an equation is written in general form it is easier to graph the equation by finding the intercepts.

Step 1: Find the x-intercept, let y = 0 then substitute 0 for y in the equation and solve for x
Step 2: Find the y-intercept, let x = 0 then substitute 0 for x in the equation and solve for y
Step 3: Plot the intercepts, label each point, and draw a straight line through these points.

This video shows how to find intercepts and use intercepts to graph linear equation.

This video shows how to graph Linear Functions by Finding the X-Intercept and Y-Intercept of the Function.

Graph Linear Equations using Slope-Intercept

We can use the slope and y-intercept to graph a linear equation.

The slope-intercept form of an equation is

y = mx + b, where m is the slope of the line and b is the y-intercept.

Step 1: Find the y-intercept and plot the point.
Step 2: From the y-intercept, use the slope to find the second point and plot it.
Step 3: Draw a line to connect the two points.

In this video, we will learn about the slope intercept formula. We look at what slope and intercept mean as well as how to graph the equation.

This video explains how to graph a linear equation given in slope intercept form.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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