Graphs and the Cartesian Coordinate System

The Cartesian Plane

The Cartesian coordinate system is a two-dimensional plane formed by two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical). The point where these axes intersect is called the origin, denoted as (0, 0). This system is fundamental for graphing equations and visualizing mathematical relationships in Precalculus.

• X-axis: The horizontal axis, typically representing the independent variable.

• Y-axis: The vertical axis, typically representing the dependent variable.

• Origin: The intersection point of the axes, coordinates (0, 0).

• Quadrants: The plane is divided into four regions called quadrants, numbered I to IV counterclockwise starting from the upper right.

Example: The point (3, -2) is located 3 units to the right of the origin and 2 units down.

Plotting Points

To plot a point on the Cartesian plane, use an ordered pair (x, y):

• Move x units left or right from the origin (along the x-axis).

• Move y units up or down from that position (along the y-axis).

Example: To plot (−4, 5), move 4 units left and 5 units up from the origin.

Applications of the Cartesian Plane

The Cartesian plane is used to:

• Graph equations and inequalities

• Visualize functions and their transformations

• Analyze geometric figures and their properties

Additional info: The grid shown is a blank template, commonly used for plotting points, graphing lines, and visualizing functions in Precalculus.