CUET UG 2025 — General Test Geometry

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

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

Formula for slope:

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

$$\text{Slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}$$Slope (m)=x2​−x1​y2​−y1​​

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Consider any two points on the x-axis:

Point 1: $(1, 0)$(1,0)

Point 2: $(5, 0)$(5,0)

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

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Applying the slope formula:

$$\text{Slope} = \frac{0 - 0}{5 - 1}$$Slope=5−10−0​

$$\text{Slope} = \frac{0}{4}$$Slope=40​

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

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

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

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

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