Chapter 13

Grappling with Graphing


Bullet Looking at lines and their special features

Bullet Investigating intersections of lines

Bullet Taking a peek at parabolas

In this chapter, I present the basics for working with lines and their equations. You find lines determined by two points and then other lines determined by a slope and a point. You see lines that meet and lines that avoid one another forever.

I also throw you a curve or two! Circles and parabolas are the most recognizable of the algebraic curves and have the most respectable equations. The basics for drawing these curves are found here.

Preparing to Graph a Line

A straight line is the set of all the points on a graph that satisfy a linear equation. When any two points on a line are chosen, the slope of the segment between those two points is always the same number.

To graph a line, you need only two points. A rule in geometry says that only one line can go through two particular points. Even though only two points are needed to graph a line, it’s usually a good idea to graph at least three points to be sure that you graphed the line correctly.

An equation whose graph is a straight line is said to be linear. A linear equation ...

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