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)
a. the slope is \square. (simplify your answer.)
b. the slope is undefined.
indicate whether the line through the points rises, falls, is horizontal, or is vertical.
the line rises from left to right.
the line is vertical.
the line is horizontal.
the line falls from left to right.

Explanation:

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$ for points $(x_1,y_1)$ and $(x_2,y_2)$

Step2: Substitute given points

Points $(3,-7)$ and $(3,2)$: $x_1=3,y_1=-7,x_2=3,y_2=2$
$m = \frac{2 - (-7)}{3 - 3} = \frac{9}{0}$

Step3: Evaluate slope validity

Division by 0 is undefined, so slope is undefined.

Step4: Classify the line

Lines with undefined slope are vertical (same $x$-value for all $y$).

Answer:

B. The slope is undefined.
The line is vertical.