## Wednesday, January 15, 2020

# How to graph inequalities

## How to graph inequalities

## Graphing Linear Inequalities

This is a graph of a linear inequality:

The inequality y ≤ x + 2

You can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2

### Linear Inequality

A Linear Inequality is like a Linear Equation (such as**y = 2x+1**) ...

... but it will have an Inequality like

**<, >, ≤, or ≥**instead of an**=**.## How to Graph a Linear Inequality

First, graph the "equals" line, then shade in the correct area.

There are three steps:

- Rearrange the equation so "y" is on the left and everything else on the right.
- Plot the "
**y=**" line (make it a solid line for**y≤**or**y≥**, and a dashed line for**y<**or**y>**) - Shade above the line for a "greater than" (
**y>**or**y≥**)

or below the line for a "less than" (**y<**or**y≤**).

Let us try some examples:

### Example: y≤2x-1

1. The inequality already has "y" on the left and everything else on the right, so no need to rearrange2. Plot

**y=2x-1**(as a solid line because y≤ includes

**equal to**)

**less than**or equal to)

### Example: 2y − x ≤ 6

1. We will need to rearrange this one so "y" is on its own on the left:
Start with: 2y − x ≤ 6

Add x to both sides: 2y ≤ x + 6

Divide all by 2: y ≤ x/2 + 3

2. Now plot

**y = x/2 + 3**(as a solid line because y≤ includes

**equal to**)

**less than**or equal to)

### Example: y/2 + 2 > x

1. We will need to rearrange this one so "y" is on its own on the left:
Start with: y/2 + 2 > x

Subtract 2 from both sides: y/2 > x − 2

Multiply all by 2: y > 2x − 4

2. Now plot

**y = 2x − 4**(as a dashed line because y> does not include equals to)

**greater than**)

The dashed line shows that the inequality does

**not**include the line**y=2x-4**.## Two Special Cases

You could also have a horizontal or vertical line:

This shows where y is less than 4 (from, but not including, the line y=4 on down)Notice that we have a dashed line to show that it does not include where y=4 | This one doesn't even have y in it! It has the line x=1, and is shaded for all values of x greater than (or equal to) 1 |

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