Question

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

Short answer

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

Step-by-step solution

Part a. Step-1 – Given

The given axis is$x-\text{axis}$.

Step-2 – To determine

We have tofind 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 tofind 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.