SAMPLE College Algebra

16

Chapter 1: Linear Functions

• The horizontal line is labeled x, and this is called the x-axis . • The vertical line is labeled y, and this is called the y-axis . • The x-axis spans from about negative 4 to about positive 4. • The y-axis spans from about negative 4 to positive 4.

2 4

y

x

− 4 − 2

2 4

− 4 − 2

A student should keep in mind that the coordinate plane shown above is displaying a sample or subset of space in 2 dimensions. This is demonstrated again below. Each of the examples below, makes use of the coordinate plane, in a different way. Fig. 1.1: − 6 . 5

2 4

2 4 6

2 4

y

y

y

x

x

− 6 − 4 − 2

2

− 2

2 4 6

x

− 4 − 2

− 4 − 2

− 4 − 2

2 4

− 2

Figure 1.1, just above, makes use of the coordinate plane to show x, between -6 and 2. Then, Figure 1.2, just above, makes use of the coordinate plane to show y, between -2 and 6. Figure 1.3, just above, makes use of the coordinate plane, to show x between -2 and 6. That the coordinate plane can be divided into 4 sections. These 4 sections are called quadrants.

2 4

• Quadrant 1 is shown in orange, labeled Q1 • Quadrant 2 is shown in blue, labeled Q2 • Quadrant 3 is shown in yellow, labeled Q3 • Quadrant 4 is shown in green, labeled Q4

y

Q2

Q1

x

− 4 − 2

2 4

− 4 − 2

Q3

Q4

Definition 1.1 — Coordinate Pair. A coordinate pair is a pair of numbers that describes the position of a point on the coordinate plane. A coordinate pair is written in parentheses. The first number is called the x-coordinate. The second number is called the y-coordinate. In the coordinate pair (3,2), the x-coordinate would be 3, and the y-coordinate would be 2.

Tip A coordinate pair is also called an ordered pair.