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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 direct Inequality is choose a direct Equation (such together y = 2x+1) ...

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... But it will have an Inequality prefer , ≤, or ≥ rather of an =.


How come Graph a direct Inequality

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

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There are three steps:

Rearrange the equation therefore "y" is top top the left and also everything rather on the right.Plot the "y=" line (make that a hard line because that y≤ or y≥, and a dashed line because that y)Shade over the line because that 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 currently has "y" ~ above the left and everything else on the right, so no need to rearrange

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

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

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


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

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

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2x - 4 " />


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

Two distinct Cases

You could additionally have a horizontal or upright line:

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