# How to Graph Linear Inequalities? (+FREE Worksheet!)

Learn how to graph linear inequalities using a testing point in a few simple steps.

## Related Topics

- How to Find Midpoint
- How to Find Distance of Two Points
- How to Find Slope
- How to Write Linear Equations
- How to Graph Lines by Using Standard Form

## Step by step guide to graphing linear inequalities

- First, graph the “equals” line.
- Choose a testing point. (it can be any point on both sides of the line.)
- Put the value of \((x, y)\) of that point in the inequality. If that works, that part of the line is the solution. If the values don’t work, then the other part of the line is the solution.

**The Absolute Perfect Book to Ace the College Algebra Course**

### Graphing Linear Inequalities – Example 1:

Sketch the graph of \(y<2x-4\).

**Solution:**

First, graph the line:

\(y=2x-4\). The slope is \(2\) and \(y\)-intercept is \(-4\).

Then, choose a testing point. The easiest point to test is the origin: \((0,0)\)

\((0,0)→y<2x-4→0<2(0)-4→0<-4\)

\(0\) is not less than \(-4\). So, the other part of the line (on the right side) is the solution.

### Graphing Linear Inequalities – Example 2:

Sketch the graph of \(y<2x-3\).

**Solution:**

First, graph the line:

\(y=2x-3\). The slope is \(2\) and \(y\)-intercept is \(-3\).

Then, choose a testing point. The easiest point to test is the origin: \((0,0)\)

\((0,0)→y<2x-3→0<2(0)-3→0<-3\)

\(0\) is not less than \(-3\). So, the other part of the line (on the right side) is the solution.

## Exercises for Graphing Linear Inequalities

### Sketch the graph of each linear inequality.

- \(\color{blue}{y < – 4x + 2}\)

- \(\color{blue}{2x + y < – 4}\)

### Download Graphing Linear Inequalities Worksheet

- \(\color{blue}{y < – 4x + 2}\)

- \(\color{blue}{2x + y < – 4}\)

**The Absolute Best Books You Need to Ace Algebra **

## Related to This Article

### More math articles

- Number Properties Puzzle – Challenge 14
- How to Scale a Function Vertically?
- Mastering the Basics: The Significance of “Algebra I for Beginners” in Your Back-to-School List
- FREE 7th Grade SBAC Math Practice Test
- Top 10 4th Grade SBAC Math Practice Questions
- Supermarket Sweep: How to Choose the Better Coupon in Aisle 7!
- Unlocking the Secrets of Triangle Angle Sum
- How to Choose the Right Visual: Models for Multiplying Fractions by Whole Numbers
- How to Evaluate Credit Reports: Personal Financial Literacy
- 4th Grade PSSA Math Practice Test Questions

## What people say about "How to Graph Linear Inequalities? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.