Question

(a) find the slope of the line passing through the points $(-2, 2)$ and $(-2, 5)$.
slope: 0
(b) find the slope of the line passing through the points $(5, 6)$ and $(5, -6)$.
slope: 0

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: Calculate slope for (a)

Substitute $(-2,2)$ and $(-2,5)$:
$m=\frac{5-2}{-2-(-2)}=\frac{3}{0}$
Division by 0 is undefined; this is a vertical line.

Step3: Calculate slope for (b)

Substitute $(5,6)$ and $(5,-6)$:
$m=\frac{-6-6}{5-5}=\frac{-12}{0}$
Division by 0 is undefined; this is a vertical line.

Answer:

(a) slope: undefined
(b) slope: undefined