Most of the lines we'll be graphing will much more complex than simple vertical and horizontal lines. There are many ways to go about graphing these, but we'll only work with the two most common methods: plotting points and slope-intercept form.
Graphing lines by plotting points isn't too rough. Just find two or more points—any (x, y) points—on the line and connect the dots.
Although we really only need two points to make a line, finding a third one is often a good idea. If all three points lie in a straight line, we can feel confident that we didn't make a mistake. If the third point doesn’t fit our line, we check our work and try again.
Let's start with a simple example:
To find three points on this line, we pick any values we want for one variable, plug them into the equation, then solve for the other variable.
Since y is already isolated in this equation, it's a good idea to start by picking values for x. This will give us a value for x and one for y, which we can plot as an (x, y) point!
Here’s a tip: in the beginning, go easy on yourself and pick nice and simple values for x, like -1, 0, and 1.
| Pick an x-value | Plug into y = 2x + 1 | Solve for y | (x, y) |
| 0 | y = 2(0) + 1 | y = 2(0) + 1 y = 0 + 1 y = 1 | (0, 1) |
| 1 | y = 2(1) + 1 | y = 2(1) + 1 y = 2 + 1 y = 3 | (1, 3) |
| -1 | y = 2(-1) + 1 | y = 2(-1) + 1 y = -2 + 1 y = -1 | (-1, -1) |
Now that we have our three points, we can plot these on a coordinate grid and connect 'em.
Look Out: although we can graph a line by only plotting two points, it's always a good idea to do at least three. If all three lie in a straight line, we can feel pretty confident that our answer is correct.