Question

How do you find the slope that is perpendicular to the line $x = 4$ ?

Answer 1

Hint : In order to determine the slope of the perpendicular to line $x = 4$ , remember the lines of form $x = a$ are the lines parallel to y-axis and the perpendicular to such lines is the x-axis or the lines parallel to x-axis. Slope of the x-axis or lines parallel to the x-axis is always equal to zero.

Complete step-by-step answer :
We are given an equation of line as $x = 4$ .
As we know, There is one most important property of plane that the graph to equation of form $x = a$ ,is always a line parallel to y-axis and passing through point $a$ on x-axis
And the slope for the y-axis or the line parallel to the y-axis is undefined.
But in this question, we have to find the slope for the perpendicular to $x = 4$ .The perpendicular to line of form $x = a$ will be a line of the form $y = a$ i.e. x-axis or a line parallel to x-axis.
Thus, the Slope for the x-axis or line parallel to the x-axis is equal to zero/0.
Therefore, the slope of the line perpendicular to $x = 4$ is equal to $0$ .
So, the correct answer is “ $0$ ”.

Note : 1.Draw the cartesian plane only with the help of straight ruler and pencil to get the perfect and accurate results.
2.Slope of line perpendicular to the line having slope $m$ is equal to $- \dfrac{1}{m}$ .
3.The slope of the vertical line is undefined or can’t be found as the denominator of the rise over run fraction is always zero.