Number Line
Recall that a number line is a
horizontal line that has points which correspond to numbers. The
points are spaced according to the value of the number they correspond
to; in a number line containing only whole numbers or integers, the
points are equally spaced.
We can graph real numbers by representing them as points on the number
line. For example, we can graph "
2
" on the number
line:
Graph of the Point 2
We can also graph inequalities on the number line. The following graph
represents the inequality
x≤2. The dark line
represents all the numbers that satisfy
x≤2. If we
pick any number on the dark line and plug it in for
x, the inequality
will be true.
Graph of the Inequality x≤2
The following graph represents the inequality
x < 2. Note
that the open circle on
2 shows that 2 is
not a
solution to
x < 2.
Graph of the Inequality x < 2
Here are the graphs of
x > 2 and
x≥2,
respectively:
Graph of the Inequality x > 2
Graph of the Inequality x≥2
An inequality with a "
≠" sign has a solution set which is all the
real numbers except a single point (or a number of single points).
Thus, to graph an inequality with a "
≠" sign, graph the entire
line with one point removed. For example, the graph of
x≠2 looks like:
Graph of the Inequality x≠2
