Discussion
Calm down. All you have to do is follow the yellow brick road, although
there probably aren't any ruby slippers in this story.
Your equation is in two variables and neither of them has an exponent of 2 or
more, so you know right off that this is going to graph as a straight line.
Now, remember back to geometry. How many points does it take to determine a
line? Two, remember?
So all you have to do is find and plot two points that are on the line, draw
a line through the two points, and you are done.
To find a point on the line, pick a value for one of the variables and solve
for the other. The reason this works is that the coordinates of any point on
the line when substituted into the equation will make the equation a true
statement. Conversely, if you substitute the coordinates of any point that is
not on the line, you will end up with a false statement.
Solution
The first thing to do is arrange the equation so that y is on the left and
everything else is on the right.
Next, pick a value for x. It doesn't matter what value you pick, so I usually
pick something that will make the arithmetic easy. Let's start with x = 0.
Substitute that value for x into the equation:
Now we can say that if x = 0, then y = -3, which means that the point (0,-3)
is on the line and we have one of the points that we need.
So let's repeat the process with another value for x. Let's try x = 1.
Substitute 1 for x into the equation:
So we can say that if x = 1, then y = -1, which means the point (1,-1) is on
the line as well.
Take your two points, plot them on a graph and draw the line all the way across
the graph through the two points. Job done -- welcome to the Emerald City.
Check Answer
Here's a picture of what you should have when you are done:
(