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Graphing 2 Variable Inequalities - Problem 3

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Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

When an inequality has one variable, this can be graphed either on a number line or on a coordinate plane. If graphing on a coordinate plane, graph using a solid line ("greater than or equal to", "less than or equal to") or a dotted line ("greater than", "less than"). Next, shade in the appropriate region to indicate that the solution falls anywhere within that shaded region.

Sometimes it's useful to graph an equation that only has one variable in the XY plane which is built for two variables.

Here is an example. Graph x is greater than 3. You guys already know that a good graph is on the number line and it would just look like this. Open circle at 3 and marking things that are greater than 3, but it's also sometimes useful to have it on the XY plane and here is how it would look.

First I want to graph the vertical line x equals 3 which looks like that, it's going vertical through the value x equals 3, then I want to change it to a dashy line because x has to be greater than 3 this doesn't count x equals 3 is not a solution, I need to like erase that kind of. And then the last thing I want to do is do some shading. I need to shade on the graph wherever x is bigger than 3, so let's see.

Here x is 1, that's smaller, 2 is smaller 3 okay 4. I want to shade this area here where I'm having 4, 5, 6, 7 these are my x values that are bigger than 3.

So both of these graphs represent the same thing this number line shows x is bigger than 3. This XY coordinate plane shows x is bigger than 3, it's just two different ways of representing the same information. So you really want to be careful when you're doing this homework problems to make sure you either ask your teacher or read the textbook carefully to see if they want you to graph it in the XY plane or just on the number line like that.

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