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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) ...

You are watching: Greater than or equal to graph

... 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.

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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)Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (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 rearrange

2. Plot y=2x-1 (as a solid line because y≤ includes equal to)

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

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1. We will need to rearrange this one so "y" is on its own on the left:


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

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

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2x - 4 " />


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:

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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=4This 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