Question

Find the slope of the line that passes through each pair of points.

$\left(a,2\right),\left(a,-2\right)$

Short answer

The slope of the line is $\infty$.

Step-by-step solution

Step 1- Given information

A pair of points $(a,2),(a,-2)$.

Step 2- Formula used

The slope formula of a line is:

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

Where, m is slope of the line which is passes through the points $(x_1,y_1),(x_2,y_2)\text{and}{x}_1\ne x_2.$

Step 3- To find the slope 

Here, $(x_1,y_1)=(a,2){\text{and (x}}_2,y_2)=(a,-2)$

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

$\begin{array}{l}\Rightarrow m=\frac{-2-2}{a-a}\\ \Rightarrow m=\frac{-4}{0}\\ \Rightarrow m=\infty \end{array}$

Hence, the slope of the line is $\infty$.