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### Graphing without the Y

```Date: 01/28/2004 at 20:43:42
From: Stephanie
Subject: Algebra

I need help with graphing inequalities.  There is a certain one that
doesn't make any sense to me.  It is:

x > -5

There is no "y", so how do I do it?
```

```
Date: 01/29/2004 at 09:48:37
From: Doctor Ian
Subject: How do you deal with a missing y?

Hi Stephanie,

There are a couple of ways to look at this.  One is to forget about
the coordinate plane, and go back to the number line.  On a number
line, you want to emphasize (by making it bolder) the part of the line
that satisfies the inequality, e.g., to graph

3 < x < 7
-

I would do this:

<--|--|--o===========*--|--|-->
1  2  3  4  5  6  7  8  9

Here the 'o' represents an open endpoint, meaning I can get almost
down to 3, but never quite there; while the '*' represents a closed
endpoint, meaning I can get all the way to 7.

Does this make sense?

Now, suppose I really want to graph this on a coordinate plane.  Let's
think for a moment about the equation of a vertical line on the plane.
That might look like

x = 4

right?  There's no y!  So what can we do?  Well, when no constraints
are placed on y, it means that y can take _any_ value at all.  In the
case of a vertical line, y can be 2, giving us the point

(4,2)

or it can be 6.3, giving us the point

(4,6.3)

and so on.  When we fill in _all_ the possible values of y, we get a
vertical line.

In the case of an inequality, we get a vertical line through each
possible value of x.  That would include when x is 4,

|
|
|
<--|--|--o==|========*--|--|-->
1  2  3  |  5  6  7  8  9
|
|

and when x is 5.3,

|   |
|   |
|   |
<--|--|--o==|===|====*--|--|-->
1  2  3  |  5| 6  7  8  9
|   |
|   |

and every other possible value of x in the specified range.  When we
fill all those lines in, what will we get?  We'll end up with a shaded
region of the plane,

o###########*
o###########*
o###########*
<--|--|--o###########*--|--|-->
1  2  o###########*  8  9
o###########*
o###########*

Here, the 'o's would normally be drawn as a dashed line, showing that
we can't quite get over to x = 3; and the '*'s would be drawn as a
solid line, to show that we can get all the way to x = 7.

Does this make sense?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations
Middle School Graphing Equations

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