# Basic Algebra

### Topics

## Introduction to :

**Graphing X-Y Points**

Chances are you have been graphing points for a long time. However, you may have been doing so on charts that look like this:

But since you are blasting ahead in math, you soon will be graphing on charts that look like this:

This is called a **Cartesian coordinate graph**. It is made up of two axes ("axes" is simply 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 1-4 (usually shown in Roman numerals) and are ordered counterclockwise starting from the upper right quadrant.

## Plotting Points on a Graph

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

The center point of the graph is called the "origin" and is written as the point (0, 0), because it is 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 three on the *x*-axis and the -6 on the *y*-axis.

Give the Cartesian coordinates of each point and name the quadrant they lie in.

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 is not in a quadrant

E. (0, 0), no quadrant

F. (4, -5), Quadrant IV

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

#### Exercise 1

In which quadrant(s) are both the x and y coordinates the same sign?

#### Exercise 2

If a point has a y coordinate of zero, which axis does it lie on?

#### Exercise 3

Do these points lie in a straight line: (-8, -1), (-6, 1), (-4, 3) and (0, 7)?

#### Exercise 4

What type of quadrilateral do these points form: (-3, 1), (4, 1), (2, -2) and (-5, -2)?