Theory:

In this lesson, you will learn the concepts that you should know about a line that is parallel to the \(x\)-axis or \(y\)-axis of the coordinate plane.
Line parallel to the \(x\)-axis
The \(y\)-coordinate of each point is \(0\) on the \(x\)-axis. Therefore, we can also say that every point on the \(x\)-axis is of the form \((x, 0)\).
For a line that is parallel to the \(x\)-axis, the equation for such a line is \(y = b\), where \(b\) is the value of the \(y\)-coordinate of any point on the line.
Example:
1. If \(b = 2\), then the equation of the line parallel to the \(x\)-axis will be \(y = 2\).
 
2. If \(b = -3\), then the equation of the line parallel to the \(x\)-axis will be \(y = -3\).
 
Graph1.png
Line parallel to the \(y\)-axis
The \(x\)-coordinate of each point is \(0\) on the \(y\)-axis. Therefore, we can also say that every point on the \(y\)-axis is of the form \((y, 0)\).
For a line that is parallel to the \(y\)-axis, the equation for such a line is \(x = a\), where \(a\) is the value of the \(x\)-coordinate of any point on the line.
Example:
1. If \(a = 1\), then the equation of the line parallel to the \(y\)-axis will be \(x = 1\).
 
2. If \(a = -2\), then the equation of the line parallel to the \(y\)-axis will be \(x = -2\).
 
Graph2.png