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In order to graph the inequality, it's fundamental to understand the coordinate system, which is a framework for specifying positions in a two-dimensional space. It typically consists of two perpendicular lines, known as axes, that intersect at a point called the origin.

The horizontal line is known as the 'x-axis' and the vertical line is called the 'y-axis'. Every point in this system can be identified by a unique set of coordinates, represented as an ordered pair \( (x, y) \). For example, the coordinates \( (2, 0) \) define a point where x is 2 units from the origin along the x-axis, and y is at the origin on the y-axis.

When graphing an inequality like \( x \geq 2 \), we use this coordinate system to precisely indicate the region that satisfies the inequality. The x-value of the ordered pairs will always be greater than or equal to 2.

Inequality notation is a means of representing the relative size or order of two values. It’s fundamental in expressing intervals or ranges of numbers and is widely used in various branches of mathematics, including algebra and calculus.

The most common inequality symbols are:

• \( < \) for 'less than',
• \( > \) for 'greater than',
• \( \leq \) for 'less than or equal to', and
• \( \geq \) for 'greater than or equal to'.

In the inequality \( x \geq 2 \), the symbol \( \geq \) denotes that the value of \( x \) is 'greater than or equal to' 2. Thus, this inequality encompasses all values of \( x \) that are 2 or higher. When graphed, this is visualized as a boundary line on the coordinate system at \( x = 2 \), including all of the region to its right.

The vertical line test is a method used to determine if a curve is a graph of a function. According to this test, if a vertical line intersects a curve at more than one point, then the curve isn't a graph of a function. However, when dealing with inequalities involving only one variable, like \( x \geq 2 \) in our example, we in fact graph a vertical line.

The vertical line at \( x = 2 \) on the coordinate system represents all possible values of \( y \) for the specified \( x \) value. Since there's no restriction on \( y \) in our inequality, \( y \) can take any value. Graphically, we depict this by drawing a straight vertical line at the x-value that \( x \) is equal to or greater than – which in our case is 2. All points on and to the right of this line satisfy the inequality, indicating that the inequality expression forms a semi-infinite region rather than a function curve.