Question

for each graph, decide if the two lines are parallel, perpendicular, or neither.
graph 1
image of two horizontal lines
○ parallel
○ perpendicular
○ neither
graph 2
image of a vertical line and a line with a positive slope
○ parallel
○ perpendicular
○ neither
graph 3
image of a vertical line and a line with a positive slope (different from graph 2)
○ parallel
○ perpendicular
○ neither
graph 4
image of a horizontal line and a vertical line
○ parallel
○ perpendicular
○ neither

Explanation:

Step1: Analyze Graph 1 slopes

Both lines are horizontal, slope $m=0$. Parallel lines have equal slopes.

Step2: Analyze Graph 2 slopes

Line 1 slope: $m_1=\frac{3}{1}=3$; Line 2 slope: $m_2=\frac{-1}{3}$. Check $m_1 \times m_2 = 3 \times \frac{-1}{3}=-1$, so perpendicular.

Step3: Analyze Graph 3 slopes

Line 1 slope: $m_1=\frac{3}{1}=3$; Line 2 slope: $m_2=\frac{2}{1}=2$. Slopes not equal, product $3 \times 2=6
eq -1$, so neither.

Step4: Analyze Graph 4 slopes

Line 1 is horizontal ($m_1=0$), Line 2 is vertical (undefined slope). Horizontal/vertical lines are perpendicular.

Answer:

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