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:

Graph 1

• Step1: Check for parallelism

Parallel lines have the same slope and never intersect. In Graph 1, the two lines are vertical and will never intersect.

Graph 2

• Step1: Check for perpendicularity

Perpendicular lines intersect at a right - angle (\(90^{\circ}\)). The lines in Graph 2 intersect at a right - angle.

Graph 3

• Step1: Check for parallelism and perpendicularity

The lines in Graph 3 have different slopes (one is vertical and the other is not) and do not intersect at a right - angle.

Graph 4

• Step1: Check for parallelism

Parallel lines have the same slope and never intersect. In Graph 4, the two lines have the same slope and will never intersect.

Answer:

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