Algebra Know-It-ALL

If a point lies exactly on one of the axes or at the origin, then it is not in any quadrant. The
quadrants are sometimes labeled with Roman numerals. In most Cartesian graphs, they’re
located like this:

• Quadrant I is at the upper right


• Quadrant II is at the upper left


• Quadrant III is at the lower left


• Quadrant IV is at the lower right

Axis increments

In a true Cartesian coordinate plane, both axes are linear, and both axes are graduated in
increments of the same size. This means that for any given axis, the change in value is always
directly proportional to the physical displacement. If we move 1/4 of an inch along an axis
and the value changes by 1 unit, then that fact is true everywhere along that axis and it is also
true everywhere along the other axis.
In a more generalized system called rectangular coordinates or the rectangular coordinate
plane, the two axes do not have to be graduated in the same increments. The value on one axis
might change by 1 unit for every 1/4 of an inch, while the value on the other axis changes by
25 units for every 1/4 of an inch. The increments we select for each axis depend on what sort
of relation or function we want to graph. It’s best to choose the increments so a graph is easy
to read.

Two Number Lines 225

–6 –2–4 246

2

4

6

–2

–4

–6

First

quadrant

Second

quadrant

Third

quadrant

Fourth

quadrant

Figure 14-3 The Cartesian plane is divided into

quadrants. The first, second, third, and

fourth quadrants are sometimes labeled

I, II, III, and IV respectively.