I'm going to use the intercepts to help me graph the boundary line.
Again, you can use any method that you want, unless the directions say
otherwise.

**When I'm working with only the boundary line,
I will put an equal sign between the two sides to emphasize that we are
working on the boundary line. ** That doesn't mean that I
changed the problem. When we put it all together in the end, I will put
the inequality back in.

**What value is y on the x-intercept?**

If you said 0, you are correct.

If you need a

*** x-intercept**

Since the *x*-intercept came out to be (0,
0), then it stands to reason that when we put in 0 for *x* to find the** y-intercept, we will get (0,
0).**

**Let's move on and plug in 1 for x to get a second solution:**

**Plug in -1 for x to get a third solution:**

**Solutions:**

Since the original problem has a __>__, this means it DOES include
the boundary line.

**So are we going to draw a solid or a dashed line for this problem? **

**It looks like it will have to be a solid line.**

**Putting it all together, we get the following boundary
line for this problem:**

Note how the boundary line separates it into two parts.

**An easy test point would be (1, 1)**. Note that it is a point
that is not on the boundary line. In fact, it is located above the boundary
line.

**Let's put (1, 1) ****into the original problem and see what happens:**

Since our **test point (1, 1) made our inequality TRUE**, this means
it is a solution.

**Our solution would lie above the boundary line**. This means
we will shade in the part that is above it.

Note that the **gray lines indicate where you would shade** your
final answer.

If we wrote this as an equation, it would be y = 3. This is in
the form *y* = *c*,
which is one of our "special" lines.

**Do you remember what type of line y = c graphs as?**

It comes out to be a horizontal line.

Every *y*'s value on the boundary line would
have to be 3.

**Solutions:**

**x**
**y**
**(x, y)**
0
3
(0, 3)
1
3
(1, 3)
2
3
(2, 3)

Since the original problem has a <, this means it DOES NOT include
the boundary line.

**So are we going to draw a solid or a dashed line for this problem? **

**It looks like it will have to be a dashed line.**

**Putting it all together, we get the following boundary
line for this problem:**

Note how the boundary line separates it into two parts.

**An easy test point would be (0, 0)**. Note that it is a point
that is not on the boundary line. In fact, it is located below the boundary
line.

**Let's put (0, 0) into the original problem and see what happens:**

Since our **test point (0, 0) made our inequality TRUE**, this means
it is a solution.

**Our solution would lie below the boundary line**. This means
we will shade in the part that is below it

Note that the **gray lines indicate where you would shade** your
final answer.

Last revised on July 31, 2011 by Kim Seward.

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