ALI - Graphing Linear Inequalities (Lesson)
Graphing Linear Inequalities
We've taken a look at 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 in graphing an inequality is to think about it like an equality. So consider how you would graph the line y = 2x - 3 and plot those points:
Before we draw our line we need to understand a few rules about the symbols used:
when using < or > draw a dashed line; this means that the values on the line do not make the inequality true so they cannot be included.
when using ≤or≥ 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.
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:
4 < 2(-1) - 3
4 < -5
This makes an "untrue" statement so we know (-1, 4) is not a part of the solution set. So now we will shade the side opposite from the point (-1,4).
Watch this video for some more practice.
Graphing Linear Inequalities Practice
What is the inequality for each graph below?
1. 2.
3.
4. 5.
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
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