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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 often make extra work for yourself, and you'll frequently 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: The first column will be where you choose your input (x) values; the second column is where you find the resulting output (y) values. Together, these make a point, (x, y).

Pick some values for x. It's best to pick at least three value, to verify (when you're graphing) that you're getting a straight line. ("Linear" equations, the 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!)

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 may 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:   Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved

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. That's not a rule, but it's often a helpful method.

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

Some people like to add a third column to their T-chart to give room for a clear 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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