Question

fill in the blanks below.
(a) find the slope of the line passing through the points (-2, 1) and (-2, -2).
slope:
(b) find the slope of the line passing through the points (-6, -2) and (4, -2).
slope:

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: Solve part (a)

For points \( (-2, 1) \) and \( (-2, -2) \), \( x_1=-2, y_1 = 1, x_2=-2, y_2=-2 \).
Substitute into slope formula: \( m=\frac{-2 - 1}{-2 - (-2)}=\frac{-3}{0} \). Division by zero is undefined, so slope is undefined.

Step3: Solve part (b)

For points \( (-6, -2) \) and \( (4, -2) \), \( x_1=-6, y_1=-2, x_2 = 4, y_2=-2 \).
Substitute into slope formula: \( m=\frac{-2 - (-2)}{4 - (-6)}=\frac{0}{10}=0 \).

Answer:

(a) undefined
(b) \( 0 \)