Question

What is the slope of the y-axis?

Answer 1

Hint: In this question, we have to find the slope of the y-axis. Read about how to calculate the slope. Then, find the angle that y-axis makes with the x-axis. Find the tangent of the angle that is made between the both axes. This will be your answer.

Complete step-by-step solution:
We have been asked to find the slope of the y-axis. First, let us read about what slope is.
What is slope?
Basically, the slope of a line is a measure of the steepness of the line. It describes both the direction and the steepness of the line. Mathematically, it is calculated as “rise over run”.
Slope$ = \dfrac{{\vartriangle y}}{{\vartriangle x}}$. Also, slope is the tangent of the angle a line makes with the x-axis.
Moving towards the question,
X-axis is a horizontal axis and y-axis is a vertical axis. They both make an angle of $90^\circ $ with each other. It can be shown in the figure below:

As we read before, slope is the tangent of the angle a line makes with the x-axis. Here, the line is the y-axis. And y-axis makes $90^\circ $ with x-axis. Therefore, slope$ = \tan 90^\circ $. And, we know that the value of $\tan 90^\circ $ is undefined.

Therefore, the slope of y-axis is undefined.

Note: We can also use the formula, Slope$ = \dfrac{{\vartriangle y}}{{\vartriangle x}}$ to find the slope of the y-axis. Let us assume any 2 points that lie on the y-axis. Let two points be $\left( {0,k} \right)$ and $\left( {0,p} \right)$. Putting the values in the slope,
Slope$ = \dfrac{{\vartriangle y}}{{\vartriangle x}}$$ = \dfrac{{p - k}}{{0 - 0}} = \dfrac{{p - k}}{0}$.
Since the denominator is 0, the slope is undefined.
Hence, we can also use this formula to find the slope of the y-axis.