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Graphing Overview (page 1 of 3)

Sections: Straight lines, Absolute values & quadratics, Polynomials, radicals, rationals, & piecewise

In this overview, we will start with graphing straight lines, and then progress to other graphs. The only major difference, really, is in how many points you need to plot in order to draw a good graph. But those increased numbers of points will vary with the "interesting" issues related to the various types of graphs.

Before we get started, though, let me say this: You should do NEAT graphs, which means that you should be using a ruler. If you don't have a ruler, go get one. Now. It will help immensely, and you can get major "brownie points" from your instructor. And, no, using graph paper does NOT excuse you from using a ruler.

Straight lines

Suppose you have "y = 3x + 2". Since this has just "x", as opposed to "x2" or "|x|", this graphs as just a plain straight line (because it is a linear equation). The first thing you need to do is draw what is called a "T-chart". It looks like this:   Copyright © Elizabeth Stapel 1999-2011 All Rights Reserved


Then you will pick values for x, plug them into the equation, and solve for the corresponding values of y.  Don't forget to pick negatives for x; using only positive numbers can be misleading later on, so it's a bad habit to get in to now. Also, try to plot at least three points. It's just safer that way: if you mess up on one point, you'll know, because it's dot won't line up with the others. This is what this looks like:

    T-chart with values listed

Some people like to add a third column, in which they write down what the actual plot-points are, like this:

    T-chart with values and points listed

Note that, if you're using a graphing calculator, you can probably have the calculator fill in the T-chart for you. Check your manual for a "TABLE" utility, or just read the chapter on graphing. Once you know how to use this utility, then you can just copy your T-chart from the calculator screen.

Now that you have your points, draw a NICE NEAT set of axes. This means drawing an EVEN, CONSISTENT scale on the axes (evenly spacing the ticks for the numbers), and maybe even labelling the axes. Draw arrows on the ends of the axes where the numbers are getting bigger (that's what the arrows stand for, ya know!), and draw arrows NOWHERE ELSE. For comparison:

This is a good graph.

This is a bad graph.



(By the way, did you notice how the tickmarks for "5" and "10" on the axes above are longer than the others? That's not something you have to do, but it can be very helpful when counting off to graph your points. Just a tip...)



Then plot your points...


 graph with three points plotted



...and connect the dots:


 graph with line drawn

So this is a nice straight line, going uphill (which we expected, because it has a positive slope of m = 3) and crossing the y-axis at the y-intercept of y = 2.


Sometimes they give you an equation like "2y – 4x = 3". The first thing you want to do is solve this equation for "y =".This works like this:

    2y – 4x = 3
            2y = 4x + 3

              y = 2x + 1.5

Then you graph as usual.

Sometimes you want to be more careful about the values you pick for x. For instance, suppose you have "y = ( 2/3 )x + 4". In this case, make life easier for yourself by choosing x's that are multiples of 3, so you can cancel out the denominator and avoid fractions. I mean, choosing x = 5 isn't wrong, but x = 3 would be nicer to work with in this particular problem. (For further information, review the lesson on "Graphing LInear Equations".)

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Cite this article as:

Stapel, Elizabeth. "Graphing Overview: Straight Lines." Purplemath. Available from Accessed


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