Question

for each graph, decide if the two lines are parallel, perpendicular, or neither.
graph 1
grid with a vertical line and a horizontal line
○ parallel
○ perpendicular
○ neither
graph 2
grid with a slanted line and a horizontal line
○ parallel
○ perpendicular
○ neither
graph 3
grid with two horizontal lines
○ parallel
○ perpendicular
○ neither
graph 4
grid with two slanted lines intersecting
○ parallel
○ perpendicular
○ neither

Explanation:

Step1: Analyze Graph 1

One line is horizontal (slope $m_1=0$), the other is vertical (slope $m_2$ is undefined). Horizontal and vertical lines are perpendicular.

Step2: Analyze Graph 2

Calculate slope of first line: $m_1=\frac{-1}{2}$, slope of second line: $m_2=0$. Products are not $-1$, slopes not equal.

Step3: Analyze Graph 3

Both lines are horizontal, so their slopes are equal ($m_1=m_2=0$). Equal slopes mean parallel lines.

Step4: Analyze Graph 4

Calculate slope of first line: $m_1=\frac{-1}{3}$, slope of second line: $m_2=\frac{-1}{3}$. Slopes are equal, so lines are parallel.

Answer:

Graph 1: Perpendicular
Graph 2: Neither
Graph 3: Parallel
Graph 4: Parallel