Home
#### Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test
#### Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator
#### Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets

Home » Inequalities » Graphing Inequalities

# Graphing Inequalities

## Example 1

## Example 2

## Example 3

## Are You Still Having Trouble Graphing Linear Inequalities?

# Like This Page?

## Other Pages You Might Like

Graphing inequalities is very similar to graphing linear equations. Once your linear equation is graphed, you then must focus on the inequality symbol and perform two more steps. It's pretty easy and fun. Stick with me and you'll have no problems by the end of this lesson.

This is a graph for a linear inequality. Notice how we have a boundary line (that can be solid or dotted) and we have a half plane shaded. (Hint: These are the two extra steps that you must take when graphing inequalities.)

In order to succeed with this lesson, you will need to remember how to graph equations using slope intercept form.

There will be two additional steps that you must take when graphing linear inequalities.

As shown in this image, the first step will be to determine whether you will use a solid boundary line or a dashed boundary line. The inequality symbol will help you to determine the boundary line.

If the inequality symbol is greater than or less than, then you will use a dotted boundary line. This means that the solutions are NOT included on the boundary line.

If the inequality symbol is greater than **or equal to** or less than **or equal to**, then you will use a **solid line** to indicate that the solutions are included on the boundary line.

The second step will be to determine which half plane to shade.

If this all sounds confusing, don't worry.... Take a look at the examples below and it will all make sense.

So... first let's take a look at our graphing symbols. You may want to keep this handy for a reference.

Our first example will demonstrate how to draw your boundary line and how to choose a test point in order to shade your graph. These are the two additional steps that we take when graphing inequalities. Take a look.....

Did you notice how our boundary line was a dotted line because of the less than symbol that was used in the inequality?

Also, you may have realized that you shade below the dotted line because of the less than symbol in the inequality. However, if you are unsure you can always choose a test point. I always use the point (0,0) if it's not on the line.

Substitute (0,0) into the original inequality. If the math sentence is true once you substitute (0,0), then that means that (0,0) is a solution and you shade the half plane that contains (0,0). If the math sentence is false when you substitute (0,0), then that means that (0,0) is not a solution and the other half plane (or the side of the line that does not contain (0,0) should be shaded.

For this second example, we'll need to rewrite the equation so that it's in slope intercept form before we graph. Also take note that the sign is greater than or equal to, so we will graph a solid line this time instead of a dotted line. This example will also demonstrate how to choose three solutions to the inequality.

Our last example reinforces how you must REVERSE THE SIGN if you MULTIPLY or DIVIDE by a negative number! Let's take a look.

Want to try a few on your own? Try these practice problems.

Enter your inequality and click "Draw".

- Solving Inequalities Practice Problems
- Solving Inequalities in One Variable

Word Problems - Compound Inequalities Introduction.
- Solving and Graphing Compound Inequalities (1)
- Solving and Graphing Compound Inequalities (2)
- Solving Systems of Inequalities
- Graphing Systems of Inequalities

Practice Problems - Systems of Inequalities Word Problems
- Systems of Inequalities Word Problems

Practice Problems

Sign Up for Algebra Class E-courses

Click here to retrieve a lost password.

Custom Search

Most Popular Pages

Dear Karin,

*I am a homeschool mom of five who struggled with finding a solid algebra program for my older boys until I came upon your algebra class. Your tutorials are straight forward and detailed. Your assignments are designed in such a way that we can spend extra time on what my children need to and move on when they understand something more easily.*

* I am a math-lover myself and am excited that you have finished part 2 of this course. My boys are understanding algebra in a way that they never were able to with other courses due to the detail and care that are in each of your lessons. I also appreciate that you are available to answer questions. *

Thank you,

Jacqui Coleman

Dear Karin,

*Finding your site was such a blessing to me! I
have been out of school for 13+ years and finding out that my next
course would be Algebra scared me to death!*

* I have now found a new
love of learning for algebra--something I never thought would happen.
After indulging in the section of functions, I decided to explore
other areas that I have just learned. It made areas such as
inequalities and graphing so much easier to grasp!*

* I just wanted to
thank you for your passion and dedication for helping others! I also
love the fact that you add in some humor, too. I have shared your site
with classmates and hope they take an opportunity to look into it as
well! Thank you----*

With greatest respect,

Dani

Hi Karin,

*I just spent 3 hours doing Unit 5 Lessons 1 & 2 because that is what I am learning at school this week, and cannot believe my progress. I so wish I would have found your course sooner. It is amazing. You explain everything in such clarity it's like night and day.
Thank you so much for getting me started. I am so happy you can't believe it.
You are the best instructor ever!*

Thanks again.

Joe

- FREE Solving Equations E-course
- Algebra Class E-course
- Algebra Class Products
- Algebra Practice Test
- Algebra Readiness Test
- Homework Answer Calculator
- Practice Worksheets

- Site Map
- Pre-algebra Refresher
- Solving Equations
- Graphing Equations
- Writing Equations
- Systems of Equations
- Inequalities
- Functions
- Exponents & Monomials
- Polynomials
- Quadratic Equations
- Algebra 1 Final Exam

? ## Subscribe To This Site

Then why not use the button below, to add us to your favorite bookmarking service?

Copyright © 2009-2014 Karin Hutchinson ALL RIGHTS RESERVED

## Comments

We would love to hear what you have to say about this page!