What is the slope of x - axis?

The x-axis is the horizontal line in a coordinate plane where the y-coordinate is always $0$. Every point on the x-axis has the form $(x, 0)$ where $x$ can be any value.

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Slope measures how steep a line is. It represents the change in $y$ relative to the change in $x$.

Formula for slope:

$\text{Slope (m)} = \frac{\text{Change in y}}{\text{Change in x}}$

$\text{Slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}$

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Consider any two points on the x-axis:

Point 1: $(1, 0)$

Point 2: $(5, 0)$

Both points have $y = 0$ since they lie on the x-axis.

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Applying the slope formula:

$\text{Slope} = \frac{0 - 0}{5 - 1}$

$\text{Slope} = \frac{0}{4}$

$\text{Slope} = 0$

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The x-axis is a horizontal line. Horizontal lines have no vertical change, meaning $y$ remains constant. When the change in $y$ equals $0$, the slope equals $0$.

Horizontal lines (like the x-axis) have slope $= 0$

Vertical lines (like the y-axis) have slope $=$ undefined

Therefore, the slope of the x-axis is $0$.