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Here we have a linear equation in two variables, and we want
to graph it.
So the first thing we're going to do is find some ordered
pairs to graph.
And we'd like to find 3, because it's better to have
three points so that you can see if all three of them line
up together to see if you really do
have a straight line.
All of the graphs that we're going to be doing this
semester will be straight lines.
So if you ever get three points that are not lined up,
you know that you need to do the calculations again.
So let's start off by choosing 0 for x and then finding the y
that goes with that, and that will be one ordered pair.
Remember you can choose anything at all that
you want for x.
And I usually choose 0 for x, then I choose 0 for y after,
and then I just pick one other point--
anything that's easy.
So first of all, x is 0.
If x is 0, the equation becomes 0 takeaway y equals 2,
which is the same as negative y equals 2.
Divide both sides by negative 1, and we get y is minus 2.
So when x is 0, y is minus 2.
That's our first ordered pair.
Now we put in y is 0.
Now we're going to find the x that goes with that.
If y is 0, the equation becomes x minus 0 equals 2, or
x equals 2.
When y is 0, x is 2.
That's our second ordered pair.
And we could stop and draw these two on a graph and put a
straight line through them, but then we won't really know
if we have the correct straight line.
So we really should get a third point.
And I'll just pick x is 4.
How about that?
x is 4.
Equation becomes 4 takeaway y equals 2.
So now we solve the linear equation for y, and that'll
give us the y value that goes with x is 4.
So takeaway 4 on both sides.
We get negative y equals minus 2.
Divide both sides by a negative, and we
get y equals 2.
When x is 4, y is 2.
Now we're able to graph the equation.
And it's good to use graph paper.
That way the line will come out somewhat straight.
So we have our x-axis horizontal, y-axis vertical.
And I'll make every square equal to 1.
So if x is 0--
so we start at the origin and we move 0 for x, y is minus 2.
So we go down 2.
There's our first point.
x is 2.
So start at the origin.
Go 2 to the right, because it's a positive 2 for x.
And then y is 0, which means don't move at all vertically.
And then x is 4.
Start at the origin.
Go 1, 2, 3, 4 to the right.
y is 2, positive 2, so we go up 2.
Then we get 4, 2.
There's our other point.
And they all line up, which means we do
have a straight line.
And we put a line through it using any straight edge that
you have hanging around.
And there's our graph.