Question

for each graph, decide if the two lines are parallel, perpendicular, or neither.
graph 1
graph 2
graph 3
graph 4
parallel
perpendicular
neither
parallel
perpendicular
neither
parallel
perpendicular
neither
parallel
perpendicular
neither

Explanation:

Step1: Analyze Graph 1

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

Step2: Analyze Graph 2

Both lines are vertical, so they have identical undefined slopes, meaning they are parallel.

Step3: Analyze Graph 3

One line has slope $m_1=1$, the other has slope $m_2=-1$. Since $m_1 \times m_2 = (1)(-1) = -1$, the lines are perpendicular.

Step4: Analyze Graph 4

One line has slope $m_1=-1$, the other has slope $m_2=-\frac{1}{3}$. Slopes are not equal, and their product $(-1)(-\frac{1}{3})=\frac{1}{3}
eq -1$, so they are neither.

Answer:

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