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

Linear Inequality

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

You are watching: Which linear inequality is represented by the graph? y > 2x + 2 y ≥ x + 1 y > 2x + 1 y ≥ x + 2

... However it will have actually an Inequality choose , ≤, or ≥ rather of an =.

How to Graph a straight Inequality

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

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There space three steps:

Rearrange the equation so "y" is ~ above the left and everything rather on the right.Plot the "y=" heat (make that a hard line for y≤ or y≥, and also a dashed line because that 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 try some examples:

Example: y≤2x-1

1. The inequality already has "y" top top the left and also everything rather on the right, therefore no have to rearrange

2. Plot y=2x-1 (as a heavy line due to the fact that y≤ includes equal to)


3. The shade the area listed below (because y is less than or equal to)


1. Us will need to rearrange this one for this reason "y" is on its own on the left:

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


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

2x - 4 " />

The dashed line shows that the inequality walk not include the heat y=2x-4.

Two one-of-a-kind Cases

You could likewise have a horizontal or vertical line:

This reflects where y is much less than 4 (from, however not including, the line y=4 on down)Notice that we have actually a dashed line to display that it does not encompass where y=4This one doesn"t even have y in it!It has the heat x=1, and is shaded because that all worths of x better than (or equal to) 1