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Graphing Overview (page 1 of 3)

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

We will start with graphing straight lines, and then progress to other graphs. But the only major difference, really, is in how many points you need to plot in order to draw a good graph.

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. It will help immensely, and will get you major "brownie points" with your instructor. And, no, using graph paper does NOT excuse you from using a ruler.   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

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 we need to do is draw what is called a "T-chart". It looks like this:

Then we will pick values for x, and solve for y.  Don't forget to pick negatives for x; using only positives can be misleading later on, so it's a bad habit to get in to. Also, try to plot at least three points. It's just safer that way (if you mess up on one, you'll know, because it won't match up with the others). This is what this looks like:

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

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 we have our points, we draw a NICE NEAT set of axes. We draw an EVEN, CONSISTENT scale on the axes (evenly spacing the ticks for the numbers), and we maybe even label the axes. And we draw arrows on the ends of the axes where the numbers are getting bigger (that's what the arrows stand for, ya know!), and we draw arrows NOWHERE ELSE. For comparison:

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

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.

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