91Ó°ÊÓ

When we talk about a vertical line in mathematics, we refer to a straight line that runs up and down, parallel to the y-axis on a graph. It has a unique characteristic which differentiates it from other types of lines. In a vertical line, the x-value is fixed while the y-value can be any number.
For example, in the equation \(x = 3\), the x-value is always 3, no matter what the y-value is. It means if you pick any point on the vertical line represented by \(x = 3\), its x-coordinate will always be 3. The y-coordinate can be anything like 0, 1, 2, -1, etc.
This is why when plotting a vertical line, you only need to plot points such as (3,0), (3,1), (3,2), and so on, and then connect these points with a straight line.
Remember: vertical lines have an undefined slope because there is no horizontal change, only vertical change.

A Cartesian plane, often called a coordinate plane, is a two-dimensional plane formed by the intersection of a vertical line called the y-axis and a horizontal line called the x-axis. It is named after the French mathematician René Descartes.
The plane is divided into four quadrants. These quadrants are determined by the intersection of the x and y axes, which meet at the origin (0,0). The quadrants are as follows:

• Quadrant I: both x and y are positive.
• Quadrant II: x is negative, y is positive.
• Quadrant III: both x and y are negative.
• Quadrant IV: x is positive, y is negative.

Coordinates are used to define the position of points on the Cartesian plane. These coordinates are written as ordered pairs (x, y). Each pair gives you the exact spot on the plane where the point lies. For instance, the point (3, 2) is 3 units to the right of the origin and 2 units up.

Linear equations are equations involving two variables that make a straight line when graphed on a Cartesian plane. They are generally written in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
However, when you encounter equations of the form \(x = a\), it represents a special case of a linear equation. Here, \(x\) is a constant and does not depend on \(y\). This equation graphs as a vertical line that intersects the x-axis at the point (a, 0).
Let's break it down to better understand:

• The term 'linear' means it graphs a straight line.
• In the equation \(x = 3\), since there is no y-variable, the line is vertical at x = 3.
• All points on this line have the x-coordinate equal to 3, while the y-coordinate can be any value.

Knowing how to recognize and graph various forms of linear equations is an essential skill in understanding more complex mathematical concepts.