91Ó°ÊÓ

The x-axis is a fundamental part of the Cartesian coordinate system. It is the horizontal number line that, along with the vertical y-axis, creates a plane where we can plot points, lines, and curves.
In the Cartesian coordinate system, any point is defined by an ordered pair \(x, y\).
Here, the x-value describes the position along the x-axis.
The y-value, on the other hand, tells us the position along the vertical y-axis.
Lines that run parallel to the x-axis are unique because they maintain a constant y-value for all x-values.
They don't rise or fall, and thus have no incline.
For example, if a line passes through the point \((-3, -6)\) and is parallel to the x-axis, it will extend indefinitely to the left and right while continuously passing through y = -6.

The slope of a line is a numerical measure of its steepness.
It shows how much a line rises or falls as it moves from left to right.
Mathematically, the slope is expressed as \((m)\), calculated by \(m = \frac{\Delta y}{\Delta x}\), where \Delta y\ is the change in y-coordinates, and \Delta x\ is the change in x-coordinates.
A horizontal line, like one parallel to the x-axis, does not rise or fall.
Its y-coordinate remains constant, indicating a slope of zero \(m = 0\).
This means there is no vertical change as x changes, or \(rac{0}{\Delta x} = 0\).
Thus, a line parallel to the x-axis is perfectly flat.

The equation of a line describes its path in mathematical terms using the formula typically written as \(y = mx + b\).
Here, \(m\) represents the slope of the line, and \(b\) represents the y-intercept where the line crosses the y-axis.
For lines parallel to the x-axis, the slope \(m\) is zero, simplifying the equation to \(y = c\).
In this form, \(c\) is the constant value of the y-coordinates the line sits on.
This means the line goes straight across the plane, maintaining the same y-value.

• For instance, a line that passes through \((-3, -6)\) parallel to the x-axis would have the equation \(y = -6\).
• There is no need for an x-component since the slope doesn’t change with x.

Thus, any point on this line would have a y-coordinate of -6, confirming that it remains parallel to the x-axis.