Question

3.2 slope of a line homework
score: 25/27 answered: 25/27
question 26
determine whether the lines are parallel, perpendicular, or neither parallel nor perpendicular.
y = -8
y = -4
○ parallel
○ perpendicular
○ neither

Explanation:

Step1: Analyze the slope of \( y = -8 \)

The equation \( y = -8 \) is a horizontal line. The slope of a horizontal line is \( 0 \) (since for any two points on the line, the change in \( y \) is \( 0 \), and slope \( m=\frac{\Delta y}{\Delta x} \), so \( m = 0 \)).

Step2: Analyze the slope of \( y = -4 \)

The equation \( y = -4 \) is also a horizontal line. Its slope is also \( 0 \) (using the same slope formula, \( \Delta y = 0 \) for any two points on this line).

Step3: Compare slopes for parallel/ perpendicular

Two lines are parallel if their slopes are equal. Since both lines have a slope of \( 0 \), their slopes are equal. Two lines are perpendicular if the product of their slopes is \( - 1 \). Here, \( 0\times0 = 0
eq - 1 \), so they are not perpendicular.

Answer:

parallel