Question

What is the slope of the line \[x=3\] ?

Answer 1

Hint: Problems of this type can be done by characterizing the given line. As, for any value of $y$ the value of $x$ is always $3$ we can take the line as a vertical straight line. Then, from the definition of slope we conclude that the slope of the line is undefined.

Complete step by step answer:
The equation of the line that we are given is a straight line which is basically a set of points on a two-dimensional plane where all the points between and extend beyond two points. A line means nothing but an object that does not have formal properties beyond length, its single dimension. A straight line has only one dimension, length and they extend in two directions forever.
The equation of the straight line that we are given is \[x=3\] .
We are supposed to find the slope of the given straight line.
$m>0$ By slope of a straight line, we mean that the value which describes both the direction and the steepness of the line. It is generally denoted by m, in the line $y=mx+c$ .
It is calculated by finding the ratio of vertical change to the horizontal change or by the tangent of the angle which the line makes with the $x$ axis.
The line is increasing if it goes up from left to right. The slope is positive, i.e., $m>0$ .
The line is decreasing if it goes down from left to right. The slope is negative, i.e., $m<0$ .
The line is horizontal if the slope is zero.
The line is vertical if the slope is not defined.
In the given line we can understand that for any value of $y$ the points on the line will lie on a vertical line as the value of $x$ will always be $3$ . Hence, we can reach the conclusion that the slope is undefined for the given straight line.

Note: We can also find the slope of the given line by directly finding the ratio of the vertical change to the horizontal change i.e., from $\dfrac{\Delta y}{\Delta x}$ but \[\Delta x~\] is always \[3-3=0~\] so the slope gives us a division by zero, which is indeterminate or undefined.