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$={\displaystyle \frac{△y}{△x}}$. 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$={\displaystyle \frac{△y}{△x}}$ 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$={\displaystyle \frac{△y}{△x}}$$={\displaystyle \frac{p-k}{0-0}}={\displaystyle \frac{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.