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.

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.)