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Study Guide

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Chances are, we've been graphing points for a long time. However, we've probably been doing so on charts that look like this:

But since we're blasting ahead in math, we'll soon be graphing on charts that look like this:

This is called a **Cartesian coordinate graph**. It's made up of two axes ("axes" is just the plural of "axis"):

- The
**horizontal**axis is called the*x*-axis. - And the
**vertical**one is the.*y*-axis

When the two axes meet, they form four **quadrants**. These are labeled as Quadrants I, II, III, and IV (usually shown in Roman numerals) and are ordered counterclockwise starting from the upper-right quadrant.

Cartesian points are written as *xy* pairs in parentheses, like so: (*x*, *y*). To graph a point, first locate its position on the *x*-axis, then find its location on the *y*-axis, and finally plot where these meet.

The center point of the graph is called the **origin** and is written as the point (0, 0) because it's located at the zero point on the *x*-axis and the zero point on the *y*-axis.

For example, to plot the point (3, -6), find the positive 3 on the *x*-axis and the negative 6 on the *y*-axis.

Practice makes perfect, so let's give the Cartesian coordinates of each point and name the quadrant they lie in, using the graph below.

A. (5, 3), Quadrant I

B. (-3, 1), Quadrant II

C. (-6, -4), Quadrant III

D. (0, -3). It lies on an axis so it's not in a quadrant.

E. (0, 0). No quadrant because it's at the origin.

F. (4, -5), Quadrant IV

G. (6.5, 0). It lies on an axis so it's not in a quadrant.

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