Chapter Five — Graphing Linear Equations in Two Variables
The Humongous Book of Algebra Problems
Number Lines and the Coordinate Plane
Which should you use to graph?
5.1 What characteristic of an equation dictates whether its solution should be
graphed on a number line or a coordinate plane?
A number line is, like any line, one-dimensional, whereas a coordinate plane
is two-dimensional. Equations with one variable are one-dimensional, so their
solutions must be graphed on a number line. Equations with two different
variables have a two-dimensional graph.
5.2 Graph the values w = 6, x = –5, y = , and z = on the number line in
Figure 5-1: Plot w, x, y, and z on this number line.
To plot w, count six units to the right of 0 and mark the value with a solid dot.
Because x is negative, it should be ﬁve units to the left of 0. Plot y two-thirds of a
unit to the right of 0 ( of the distance from 0 to 1 on the number line). It
is easier to plot z if you ﬁrst convert it from am improper fraction into a mixed
number: . It is located 2.25 units to the left of 0, two full units and
then one-fourth of a unit beyond that. All four values, w, x, y, and z, are
illustrated in Figure 5-2.
Figure 5-2: Negative values, like x and z, are located left of the number 0, and positive
values, like w and y, are located to the right of 0.
5.3 Solve the equation 2x – 3(x + 1) – 5 = –6 and graph the solution.
Use the method described in Problems 4.1–4.36 to isolate x and solve the
equation. Begin by distributing –3 through the parentheses, then combine like
terms, isolate x on the left side of the equation and eliminate the coefﬁcient of x.
A line is
because it just
travel, left and right
along the line. On
a coordinate plane,
however, you can
and vertically, in two
dimensions. Think of an
ant crawling along a
stick as opposed to
on a piece of
not sure how
to do this, check