Before we get into the complexities of graphing lines, we are going to first introduce how to graph the really simple lines, those that are completely vertical or horizontal.
Take a look at these lines:
What do you notice about all of these horizontal lines? If you answered that they are all y = something, then you’re right.
Horizontal lines are all in y = A form, where A is any real number.
This is because you are graphing all points where y equals some number. Let's look at y = 3 a little more closely.
If we pick any point on the line, like the three shown, the y-coordinate will be 3. The x-coordinate will vary, but the y will always be 3. That's why the equation for this line is y = 3.
Now take a look at these lines:
Have you noticed that these lines were all vertical – and in the form x = something? Not surprisingly, this is because all points that lie on a vertical line have the same x-coordinate.
Here are some points on the line x = -1:
If we want to graph the line y = -2, all we need to do is plot all the points that have a y-coordinate of -2 and connect them, sort of like connect the dots.
We didn't really need to graph all of those points, two would have been sufficient, but we like to make a point (no cheesy math pun intended).