How do I graph a line/linear equation?

Question

For example, how do I graph y = 2x + 4?

Answer 1

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Answer 2

I would like to apologize in advance; I cannot include images in this answer because of the limitations of the program!

We graph linear equations (equations with two variables but neither of them are raised to a power (for example squared)) on a coordinate plane. This is the mathematical term for a grid with an x-axis and a y-axis. If you are still uncertain of what this is, google it (coordinate plane).

In order to graph, you need a series of ordered pairs or points that you know the x and y coordinates of. Let's think about the equation y = 2x + 4. You can find points on this line by solving the equation for various values of x.

If x is 1? y = 2(1) + 4 = 6. The point to graph is (1,6).

If x is 2? y = 2(2) + 4 = 8. The point to graph is (2,8).

If x is 3? y = 2(3) + 4 = 10. The point to graph is (3,10).

If x is -1? y = 2(-1) + 4 = 2. The point to graph is (-1,2). Don't just stick with the positives! Check negative numbers too!

Once you find each point, plot it on your graph. Be sure to label your axes so that we know what the value of each line is (y axis and x axis). Also, be deliberate about what you're choosing as your increment on you axes. For this equation, it would make sense to go up by one or two on both axes. However, sometimes it makes sense to choose different increments for each axis or to use a number like 1000 instead of 1.

Continue solving the equation and plotting points until you are sure you know what the pattern is. In this example, I would be able to clearly see a line after 4 points. If you are graphing a linear equation, your points should always form a line. This line will go on forever in both directions (unless the problem tells you something different) so use a ruler to connect your dots and add arrows to both ends to show it is continuous.

Things to check before you are done:

1. both axes are labeled (if there aren't units in the problem, label them x and y) and have even increases/increments. They don't have to be the same as each other, but they must be consistent for the x axis and for the y axis.
2. It's always a good idea to label your points. Simply write the ordered pair (3,10) next to that point.
3. Arrows on the ends of your axes and your line!
4. Label your line: write the equation somewhere near the line. This is especially important if you are graphing multiple lines on the same coordinate plane.
5. Many math teachers don't require titles, but formal graphs must have either a title or a figure number and caption. Check to see what your requirements are.