Question

find the slope of the line that passes through the pair of points.
(2, -7), (2, 7)

a) 0

b) $-\frac{7}{2}$

c) $\frac{7}{2}$

d) undefined

Explanation:

Step1: Recall slope formula

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

Step2: Identify coordinates

Here, \( x_1 = 2 \), \( y_1=-7 \), \( x_2 = 2 \), \( y_2 = 7 \).

Step3: Substitute into formula

Substitute into the slope formula: \( m=\frac{7 - (-7)}{2 - 2}=\frac{7 + 7}{0}=\frac{14}{0} \). Division by zero is undefined, so the slope is undefined.

Answer:

D) undefined