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

Linear Inequality

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

You are watching: Greater than or equal to graph

... But it will have actually an Inequality favor , ≤, or ≥ rather of one =.

How come Graph a direct Inequality

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

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There room three steps:

Rearrange the equation therefore "y" is ~ above the left and also everything rather on the right.Plot the "y=" heat (make that a heavy 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 for a "less than" (y

Let us shot some examples:

Example: y≤2x-1

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

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


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


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

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


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

2x - 4 " />

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

Two one-of-a-kind Cases

You could likewise have a horizontal or vertical line:

This reflects where y is less than 4 (from, but not including, the heat y=4 ~ above down)Notice the we have actually a dashed heat to present that that does not incorporate where y=4This one doesn"t even have y in it!It has actually the heat x=1, and also is shaded for all values of x greater than (or same to) 1