 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) 2x - 4 " />

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