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The Cartesian coordinate system is the foundation for graphing points on a coordinate plane. It consists of two number lines, one horizontal and one vertical, that intersect at a right angle.
This intersection point is known as the origin, and it divides the plane into four quadrants.

• The horizontal number line is called the x-axis.
• The vertical number line is called the y-axis.

Each point in this system is described using a pair of numbers called coordinates, usually written as \( (x, y) \). The first value, the x-coordinate, represents the position on the x-axis, while the second value, the y-coordinate, indicates the position on the y-axis. Understanding these coordinates is crucial for correctly placing points in the plane and interpreting their positions relative to the axes.

The x-axis plays a crucial role in the Cartesian coordinate system. It is the horizontal line that extends infinitely in both directions and is used to measure the horizontal distance of a point from the origin.
If a point has a y-coordinate of zero, this means the point lies directly on the x-axis. The role of the x-coordinate is to show how far and which direction (right if positive, left if negative) the point is located from the origin.
To illustrate this using the point \( (-6,0) \):

• The x-coordinate is -6, representing a movement to the left of the origin.
• The y-coordinate is 0, indicating that the point is right on the x-axis.

Therefore, \( (-6,0) \) can be found directly on the x-axis, aligning with the concept that all points with a y-coordinate of zero lie on it.

Graphing points is one of the fundamental tasks when working with the Cartesian coordinate plane.
To graph a point, follow these steps:1. Start at the origin \( (0, 0) \).2. Move along the x-axis according to the x-coordinate of the point: - Move right if the x-coordinate is positive. - Move left if the x-coordinate is negative.3. From there, move parallel to the y-axis based on the y-coordinate: - Move up if the y-coordinate is positive. - Move down if the y-coordinate is negative.
For example, to graph \( (-6, 0) \):

• Start at the origin.
• Move 6 units to the left on the x-axis because of the \( -6 \) x-coordinate.
• Stay on the x-axis as the y-coordinate is 0.

This simple procedure helps in accurately plotting points and understanding their relative positions on the coordinate plane.