Chapter 5
GRAPHING LINEAR EQUATIONS IN TWO VARIABLES
After you solve equations, it is useful to represent those solutions graphi-
cally. Unlike the equations in Chapter 4, some linear equations have more
than one solution. In fact, most linear equations in two variables have an
infinite number of solutions, and the most effective way to present those
solutions is visually, by means of a graph. In this chapter, you learn how to
graph the solutions of equations that contain only one variable (usually x),
equations that contain two variables (usually x and y), and absolute value
equations in two variables. Aside from these graphing techniques, the prob-
lems also introduce the concept of slope, the key component necessary to
create linear equations, a task undertaken in Chapter 6.
Graphs allow you to visualize the solutions of an equation. There’s
really no need to visualize a solution when there’s only one (like x = 2)
but when there are an innite number of values that make an equation
true, listing them all is impossible. Graphing them is the next best thing.
You’ll learn two ways to graph lines: using a table of values and using
intercepts. You’ll also learn how to calculate the slope of a line and
how to graph an equation containing absolute values.
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