Question

Slope of the line parallel to y-axis is
A. 1
B. $90^\circ $
C. Undefined
D. $180^\circ $

Answer 1

Hint: In this particular type of question you have to understand the process of finding out the slope of a line and also understand why there is a specific case when the line is vertical or parallel to y axis. The slope of a line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.

Complete step-by-step answer:
Slope of a line = m = $\tan \theta $
where θ is the angle made by the line with the x−axis.
For a line parallel to y−axis , $\theta $ = $\dfrac{\pi }{2}$
$\therefore m = \tan \theta =\tan\dfrac{\pi }{2} =$ undefined

Note: It is important to note that the slope of y axis is not infinity . It's undefined . To be precise, as the slope of the line approaches the vertical it increases (positively or negatively depending on the angle) without bound . This is because no matter how much their height ( position on the y-axis ) changes , their position on the x-axis never does . This means that even if their rise is infinite, their run will always be 0. The concept of slope simply does not work for vertical lines. The slope of a vertical line does not exist.