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Graphing Linear Equations: Plotting
     the points and drawing the line
(page 2 of 4)

Sections: Making a T-chart, Plotting the points and drawing the line, Examples

Now that you have your points, you need to draw your axes. REMEMBER TO USE YOUR RULER! If you don't use a ruler, you will have messy axes and inconsistent scales on the axes, and your points will NOT line up properly. Don't "fake it" with your graphs. Get in the habit now of drawing neatly. It will save you so much trouble down the line! (And, no, using graph paper is not the same as, nor does it replace, using a ruler!)   Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved

Also, make sure you draw your axes large enough that your graph will be easily visible. On a standard-sized sheet of paper (8.5 by 11 inches, or A4), you will be able to fit two or three graphs on a page. If you are fitting more than three graphs on one side of a sheet, then you're probably drawing them too small.




    Here are my axes:


    Draw your axes

Remember that the arrows indicate the direction in which the values are increasing. Your book (and even your teacher) may draw things incorrectly, but that's no excuse for you. Arrows go on the upper numerical ends of each axis, and NOWHERE ELSE (unless you have an educator who wants it drawn wrong; then just remember the right way for later courses).

    Once I've drawn my axes, I have to label them with an appropriate scale. "Appropriate" means "one that is neat and that fits the numbers I'm working with". For instance, considering the values I'm working with, I'll count off by ones. But if I were doing a graph for a word problem about government waste, I would probably count off by hundred thousands or maybe even by millions. Adjust the scales and axes to suit the case at hand. And ALWAYS use a ruler to make sure that your tick-marks are even!




    Here's my scale:


    Draw your scales

Note that I've made every fifth tick-mark a bit longer. This isn't a rule, but I've often found it helpful for counting off the larger points;it's more of a time-saver than anything else.

    By the way, if you don't use a ruler or take a modicum of care in your work, your graphs will look like what math instructors are more accustomed to seeing:



I'm not kidding; people really hand in "work" that looks like this. Please don't be one of those people!




    Now I'll plot (draw) the points I'd computed in my T-chart:


    Plot the points





    ...and then I'll finish up by connecting the dots:


    Connect the dots

Since "linear" equations graph as straight, you might as well use your ruler for this part, too. The drawing is the answer they're looking for. Once you've connected your dots, you're done with the exercise.

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Cite this article as:

Stapel, Elizabeth. "Graphing Linear Equations: Plotting the points and drawing the line." Purplemath. Available from Accessed



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