# Graphing inequalities (x-y plane)Â review

CCSS Math: HSA.REI.D.12

We graph inequalities like we graph equations but with an extra step of shading one side of the line. This article goes over examples and gives you a chance to practice.

The graph of a two-variable linear inequality looks like this:

It's a line with one side shaded to indicate which $x$-$y$ pairs are solutions to the inequality.

In this case, we can see that the origin $(0,0)$ is a solution because it is in the shaded part, but the point $(4,4)$ is not a solution because it is outside of the shaded part.

*Want a video introduction to graphing inequalities? Check out this video.*

### Example 1

We want to graph $4x+8y\leq -24$.

So, we put it in slope-intercept form:

Notice:

- We
**shade below**(not above) because $y$ is less than (or equal to) the other side of the inequality. - We
**draw a solid line**(not dashed) because we're dealing with an "or equal to" inequality. The solid line indicates that points on the line are solutions to the inequality.

*Want to see another example but in video form? Check out this video.*

### Example 2

We want to graph $-12x-4y< 5$.

So, we put it in slope-intercept form:

Notice:

- We
**shade above**(not below) because $y$ is greater than the other side of the inequality. - We
**draw a dashed line**(not solid) because we aren't dealing with an "or equal to" inequality. The dashed line indicates that points on the line are not solutions of the inequality.

### Example 3

We're given a graph and asked to write the inequality.

Looking at the line, we notice:

- $y$-intercept is $\purpleD{-2}$
- Slope is $\dfrac{\Delta y}{\Delta x}=\dfrac{4}{1}=\goldD{4}$

The

*slope-intercept form*of the inequality iswhere the "?" represents the unknown inequality symbol.

Notice:

- The graph is
**shaded above**(not below), so $y$ is greater than the other side of the inequality. - The graph has a
**dashed line**(not solid), so we aren't dealing with an "or equal to" inequality.

Therefore, we should use the greater than symbol.

The answer:

*Want to see another example but in video form? Check out this video.*