LEI - Graphing Linear Inequalities (Lesson)

Graphing Linear Inequalities

Graphing inequalities plotted points dotted line connecting dots on a graph The past few modules have been about graphing & writing linear equations (example: y = 2x - 3). When we graph these equations we are looking for the x- and y-values that make one side EQUAL the other side.

Now, we want to look at graphing linear inequalities like:

y < 2x - 3

In this statement, we care about what values of x- and y- make one side less than the other side. This is going to be a whole lot more values!

The first step to graphing an inequality is to think about it like an equality. So consider how you would graph

y = 2x - 3 and plot those points:

Before we draw our line we need to understand a few rules about the symbols used: < or > draw a dashed line; this means that the values on the line do not make the inequality true so they cannot be included!

$LaTeX: \le or\:\ge$ $\le or\:\ge$ draw a solid line; this means that the values on the line do make the inequality true so they can be included.

Since y < 2x - 3 this means we should use a dashed line.

dotted line of a linear function with a test point Since our test point did not work, we shade the side opposite from it. Now, the points on the dashed line are not included in the solution, but there are MANY points that would work. So we must determine where those points are. To do that, pick any point on the coordinate plane that is not on the graphed line to test. Let's chose (-1, 4) and substitute: