CHAPTER11 Coordinate Graphing ...............................................................
In This Chapter
- How to plot points on a
graph - How to graph lines quickly
- Finding the slope of a line
- Graphing linear equations
and inequalities
When you learned to solve equations and inequalities,
I mentioned that there should only be one variable involved.
If there are two variables in the same equation, the solution
would have to be not just a number, but a pair of numbers,
one for each variable. It turns out that if you have two
variables and only one equation, there are infinitely many
different pairs of numbers that could be solutions. You can’t
settle on just one pair. If you look at an equation like x + y
= 5, you could say x is 1 and y is 4, or x is 2 and y is 3, or x is
5 and y is 0. That’s three possible solutions already, and we
haven’t begun to talk about negative numbers or fractions yet.
A single equation with two variables has many, many possible
solutions.
When you learned to solve an inequality, you learned that
a picture of the solution set on a number line was helpful in
understanding what the solution really meant. In this chapter,
you’ll learn a system for picturing the many, many solutions
for an equation with two variables. You’ll look at the basic
idea of the system and at quick ways to draw the picture for
your particular equation. You’ll also see how a few key pieces
of information from the picture tell you what equation it
represents. Inequalities with two variables can be pictured
too, and you’ll see how those pictures compare to the pictures
of equations.