Question

find the slope of the line passing through the pair of points or state that the slope is undefined. then indicate whether the line through the points rises, falls, is horizontal, or is vertical.
(3, -7) and (3,2)

select the correct choice below and fill in the answer box within your choice

a. the slope is (simplify your answer.)

b. the slope is undefined.

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Step2: Substitute given points

Let $(x_1,y_1)=(3,-7)$ and $(x_2,y_2)=(3,2)$. Substitute into formula:
$m=\frac{2-(-7)}{3-3}=\frac{9}{0}$

Step3: Evaluate slope validity

Division by 0 is undefined, so the slope is undefined. A line with undefined slope is vertical.

Answer:

B. The slope is undefined.
The line passing through the points is vertical.