Let’s demonstrate this process by working on an example problem.

Let’s demonstrate this process by working on an example problem.

Graph the following linear inequality:

In order to graph this linear inequality start by treating it like you would any linear equation.

Temporarily replace the inequality symbol with an equal sign.

x y

-2 -1

-1 0

0 1

1 2

2 3

Remember that in order to create a t-chart, simply plug-in x values into the equation and solve for y.

y+

x+

x y

-2 -1

-1 0

0 1

1 2

2 3

Replace the equal sign with the inequality symbol.

Unlike equations where we only care about the points on the line, with inequalities we must consider the line as well as the entire area above and below the line.

When working with the ≤ or ≥ symbols we must consider points on the line as well as points above and below the line.

This is because points on the line will always satisfy the inequality.

For example, if we pick the point (0,1) and plug it into the inequality we would get 1 ≥ 1 as a result, which is always true.

In order to decide which part of the graph to shade simply pick a point above or below the line and plug that point into the inequality.

If the inequality holds true for the chosen point shade in the area containing that point, otherwise shade in the area on the other side of the line.

y+

x+(1,0)

Here I chose (1,0) as my “test point”.

Note here that we have a solid line representing the inequality because points on the line satisfy the inequality. This is the standard way to represent inequalities with the ≤ or ≥ signs.

Plug the point (1,0) into the inequality.

Simplify

Now ask yourself if this statement is true, if it is shade in the region containing this point, if not shade in the region on the other side of the line.

y+

x+(1,0)

For the point (1,0) the inequality is false, therefore we need to shade in the region on the other side of the line.

y+

x+

Here is the graph for this inequality.