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Graphing Linear Equations:
     Making a T-chart (finding plot points) (page 1 of 4)

Sections: Making a T-chart, Plotting the points and drawing the line, Examples

Graphing linear equations is pretty simple, but only if you work neatly. If you're messy, you'll only make extra work for yourself, and you'll often get the wrong answer. I'll walk you through a few examples. Follow my pattern, and you should do fine.

• Graph y = 2x + 3
     

First, you draw what is called a "T-chart":  it's a chart that looks a bit like the letter "T":     The left column will contain the x-values that you will pick, and the right column will contain the corresponding y-values that you will compute.
Label the columns:

Pick some values for x. It's best to pick at least three, to verify (when you're graphing) that you're getting a straight line. ("Linear" equations, ones with just an x and a y, with no squared variables or square-rooted variables or any other fancy stuff, always graph as straight lines. That's where the name "linear" came from!)   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

Which x-values you pick is totally up to you! And it's perfectly okay if you pick values that are different from the book's choices, or different from your study partner's choices, or different from my choices. Some values will be more useful than others, but the choice is entirely up to you. Then your y-values will come from evaluating the equation at the x-values you've chosen. And the T-chart keeps the information all nice and neat.

I'll pick the following x-values:

You can pick whatever values you like, but it's often best to "space them out" a bit. For instance, picking x = 1, 2, 3 might not give you as good a picture of your line as picking x = –3, 0, 3. It's not a rule, but a useful suggestion.

Once you've picked x-values, you have to compute the y-values:

Some people like to add a third column to their T-chart, for a listing of the points that they've found:

Which format you use is (usually) just a matter of taste. Unless your instructor specifies, either format should be fine.

(Note that, if you're using a graphing calculator, you can probably use your calculator to fill in your T-chart. Check your manual for a "TABLE" utility, or just read the chapter on graphing. Once you know how to use this utility, you can fill in your T-chart from the calculator screen.)

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