Graphing Inequalities

Date: 10/16/98 at 11:48:40
From: Mary
Subject: Graphing Inequalities

Could you explain to me how to graph inequalities that use variables?
Like when x < 2 ? I understand most of it, but I get confused as to 
which axis to graph it on, and when a dotted line is used instead of a 
solid one. I would really appreciate if you could clear these things up 
for me. Thanks!

Date: 10/16/98 at 22:50:29
From: Doctor Tom
Subject: Re: Graphing Inequalities

Hi Mary,

If you know how to graph equalities, you're most of the way to graphing 
inequalities. In your example, do you know how to graph x = 2?  That 
would just be the line at x = 2, and y = anything.

This line is where x and 2 are equal. On one side, x will generally be 
less than 2, and on the other side x will be greater than 2. Just look 
at a couple of points, one on each side of the line where they are 
equal, and check to see whether the inequality is true or not. If it's 
true on a side, it will generally be true everywhere on that side.

To know whether the line should be dotted or not, in this case it will 
be, because you are looking for values where x is strictly less than 
2. If it's equal to 2, the inequality is not satisfied, so points on 
the line where x = 2 don't work.

If the inequality had been x <= 2 (less than or equal to 2), then the 
points on the line would work, and you should draw it in solidly.

As a slightly more complicated example, look at x >= y. First draw the 
line x = y (that's a diagonal going at 45 degrees to the positive x 
and y axes, and going through the origin). Look at a point above the 
line, say x = 0 and y = 1. This does not satisfy the inequality 
because it's not true that 0 >= 1. So the values that satisfy the 
inequality are those below the line. Finally, you will draw the line 
in solidly, since if x = y you get values that work.

I hope this helps.

- Doctor Tom, The Math Forum
  http://mathforum.org/dr.math/