Question

The slope of $y$-axis is __

• A. 1
• B. -1
• C. 0
• D. Not defined

Answer 1

The correct option is D Not defined

Given, to find the slope of $y-$ axis.
Take any two points on the $y-$ axis.

x	0	0
y	3	6

We know that, slope of the line segment whose end point coordinates are $(x_1,y_1)$ and $(x_2,y_2)$ is given by
$\frac{y_2-y_1}{x_2-x_1}$

Here, $(x_1,y_1)\equiv (0,3)(x_2,y_2)\equiv (0,6)$

$\therefore$ Slope of line segment $AB=\frac{6-3}{0-0}$
$=\frac{3}{0}=\text{undefined}\text{(any value divided by zero is undefined)}$

The slope of the line $AB$ is not defined. So, Slope of $y-$ axis is not defined as line AB lies on $y-$ axis.
Option (d) is correct.