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

### 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

- \(\color{blue}{y < – 4x + 2}\)

- \(\color{blue}{2x + y < – 4}\)