Question

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

Explanation:

Graph 1

• Step1: Check parallelism

Parallel lines never intersect. These lines intersect, so not parallel.

• Step2: Check perpendicularity

Perpendicular lines intersect at \(90^{\circ}\). These lines don't (visual inspection), so neither.

Graph 2

• Step1: Check parallelism

Parallel lines never intersect. These lines intersect, so not parallel.

• Step2: Check perpendicularity

Perpendicular lines intersect at \(90^{\circ}\). These lines don't (visual inspection), so neither.

Graph 3

• Step1: Check parallelism

Parallel lines never intersect. These lines intersect (at \(90^{\circ}\)), so not parallel.

• Step2: Check perpendicularity

Perpendicular lines intersect at \(90^{\circ}\). Visual inspection shows they do, so perpendicular.

Graph 4

• Step1: Check parallelism

Parallel lines never intersect. Visual inspection shows these lines never intersect, so parallel.

• Step2: Check perpendicularity

Perpendicular lines intersect at \(90^{\circ}\). These lines don't (they don't intersect at all), so not perpendicular.

Answer:

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