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.
T-chart
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).
T-chart w/ column labels
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.
T-chart with 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. 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:
Compute the 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:
alternate format
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