Q. 2 - Geometry

Question

What can you say about the slope of (a) the x-axis? And (b) the y-axis?

Step-by-Step Solution

Answer

1. The slope of $x-\text{axis}$ is 0.
2. The slope o f$x-\text{axis}$ is undefined.

Part a. Step-1 – Given

The given axis is $x-\text{axis}$.

Step-2 – To determine

We have to find the slope of the $x-\text{axis}$.

Step-3 – Calculation

Slope formula of a line with two points  $\left(x_1,y_1\right)\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}\left(x_2,y_2\right)$is:$m=\frac{y_2-y_1}{x_2-x_1}$

Let us take any two points (-1, 0) and (2, 0) on the .

Slope of the line joining these two points, i.e., the slope of $x-\text{axis}$ is: $m=\frac{0-0}{\left(2\right)-\left(-1\right)}=0$

So, the slope of theis 0.

Part b. Step-1 – Given

The given axis is $y-\text{axis}$.

Step-2 – To determine

We have to find the slope of the $y-\text{axis}$.

Step-3 – Calculation

Slope formula of a line with two points $\left(x_1,y_1\right)\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}\left(x_2,y_2\right)\text{ is}$

$m=\frac{y_2-y_1}{x_2-x_1}$

Let us take any two points (0, 1) and (0, 3) on the $y-\text{axis}$.

Slope of the line joining these two points, i.e., the slope of is $y-\text{axis}$:

$m=\frac{3-1}{0-0}=\frac{2}{0}=\text{undefined}$

So, the slope of the is undefined.