Graphing Linear Equations Made Easy

Are you frustrated with graphing linear equations?  If you are ready to start using the equation of a line successfully, then you have come to the right place.  We make understanding the slope equation fast and easy.

The quickest way to start understanding the equations of a line is to sign up for our free trial membership.  In the members section you will have access to all of our interactive videos that deal with graphing functions.  All of the videos include study notes, practice questions, and step by step solutions; in other words, all the math help you could ever ask for.

If you prefer to continue reading, this page will focus on graphing linear equations.  In the ‘linear functions’ section we show you everything from examples of linear equations to how to find the equation of a line. If you are interested in only specific parts of this section, you can click on one of the links from the list below.

How to Start Graphing Linear Equations

We will start by looking at the rule of a linear function.  From the rule we can generate coordinates and then plot them onto a graph.  If you are not sure what the rule of a linear equation looks like, you should click on the link above (linear equations) for a list of what they look like.

Once you are sure that you have the equation of a line for a linear equation, you really only need to find two coordinates and then join them together with a straight line.  If you can use three coordinates and show that they are collinear (they form a straight line) then you know for sure that you have properly graphed a linear equation.  Let’s look at a few examples of how to graph linear functions using the rule and a table of values.

 

Example 1

Graph the following linear function using a table of values.

                                                                linear-graphs

The first thing that we need to do is generate a table of values.  We can do this by choosing numbers to replace the x-value.  Let’s look at how we can find the resulting y-values to create coordinates.

linear-graphs

We can repeat this process to make any of the coordinates that create the line to be graphed.  The table of values is an example of some of the coordinates that can be plotted on a graph.

 

linear-graphs

 

Once we have created a table of values, we can plot the coordinates and draw the line that represents the linear function.  Here we chose four points from our table of values to plot on the graph.  You can choose other points from the table of values but you will get the same graph.
linear-graphs
linear-graphs

Example 2

Graph the following linear function using a table of values.

                                                                linear-graphs

The first thing that we need to do is generate a table of values.  We can do this by choosing numbers to replace the x-value.  Let’s look at how we can find the resulting y-values to create coordinates.

 

linear-graphs

We can repeat this process to make any of the coordinates that create the line to be graphed.  The table of values is an example of some of the coordinates that can be plotted on a graph.

 

linear-graphs

 

Once we have created a table of values, we can plot the coordinates and draw the line that represents the linear function.  Here we chose four points from our table of values to plot on the graph.  You can choose other points from the table of values but you will get the same graph.

                                                                       linear-graphs
linear-graphs
                                                                       
linear-graphs

Moving Forward

If you are like us, you will want to see some more examples of graphing linear equations and how to use the equation of a line.  This page was a quick tour of examples of linear equations and how to graph them.  So, what is you next move?   

We recommend that you sign up for our free trial membership.  You can then watch all of the videos that relate to graphing linear equations.  During the video, you will get the chance to test your ability with some more challenging questions.  In addition to that you will be walked through the solutions to these questions and at the end of the video there is a helpful set of printable summary notes.

Please feel free to contact us with any of your questions, comments, or topic requests.  We are always looking to improve our services and we will respond to your emails promptly.  We want to be a part of your ongoing math success.

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