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

### Linear Inequality

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

You are watching: Which graph represents the following system of inequalities?

... However it will have an Inequality like **, ≤, or ≥** rather of an **=**.

## How to Graph a direct Inequality

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

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There room three steps:

Rearrange the equation therefore "y" is top top the left and everything rather on the right.Plot the "**y=**" heat (make the a solid line for

**y≤**or

**y≥**, and also a dashed line for

**y**)Shade over the line because that a "greater than" (

**y>**or

**y≥**)

**or below the line because that a "less than" (y**

Let us shot some examples:

### Example: y≤2x-1

1. The inequality currently has "y" on the left and also everything else on the right, so no need to rearrange

2. Plot **y=2x-1** (as a hard line because y≤ contains **equal to**)

3. Shade the area below (because y is **less than** or equal to)

1. We will should rearrange this one so "y" is ~ above its own on the left:

2. Currently plot **y = 2x − 4** (as a dashed line since y> walk not incorporate equals to)

3. The shade the area above (because y is **greater than**)

The dashed line shows that the inequality go **not** incorporate the heat **y=2x-4**.

## Two distinct Cases

You could also have a horizontal or upright line:

This mirrors where y is much less than 4 (from, yet not including, the line y=4 ~ above down)Notice the we have a dashed line to show that that does not encompass where y=4 | This one doesn"t also have y in it!It has actually the heat x=1, and is shaded for all worths of x higher than (or equal to) 1 |