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The rectangular coordinate system, also known as the Cartesian coordinate system, is a way to represent points in a plane using two numbers. These two numbers are called coordinates and are written as \( (x, y) \). The coordinate system consists of two perpendicular lines, or axes:

• The horizontal axis is called the x-axis.


• The vertical axis is called the y-axis.

Where these two axes intersect is called the origin, represented by the point \( (0, 0) \).
Each point in the plane can be located by moving horizontally to the x-coordinate and vertically to the y-coordinate.
The x-coordinate indicates how far to move right (positive) or left (negative), and the y-coordinate indicates how far to move up (positive) or down (negative). The rectangular coordinate system is essential for graphing equations and understanding geometric relationships.

A vertical line on the rectangular coordinate system is a line that goes straight up and down. This type of line is easy to recognize because it does not slant or curve.
In the context of graphing, a vertical line represents all the points where the x-coordinate is the same. This means every point on this line has the same x-value but can have any y-value. For example, if we graph the equation \(x = -4\), it means every point on this line has x = -4.
Vertical lines have these specific characteristics:

• They are parallel to the y-axis.


• They never intersect the y-axis, unless the line itself is the y-axis.


• They do not have a slope because their direction is purely vertical.

Understanding vertical lines is crucial for graphing and interpreting equations correctly.

An equation in the form \( x = c \) represents a vertical line on the rectangular coordinate system. The letter c stands for a constant value. This equation tells us that no matter what the y-value is, the x-coordinate always remains equal to c.
Let's break down the key elements of this type of equation:

• The value of c determines where the vertical line will cross the x-axis.


• If c is positive, the vertical line will be to the right of the origin.


• If c is negative, the line will be to the left of the origin.

For example, the equation \( x = -4 \) means the vertical line crosses the x-axis at -4 and extends infinitely in both positive and negative directions along the y-axis. To graph this equation:

• Find the point \( -4 \) on the x-axis.


• Draw a straight vertical line through \( -4 \) extending up and down.

This method of graphing applies to any equation of the form \( x = c \), making it a straightforward and predictable way to plot vertical lines.