Question

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

Explanation:

Graph 1

• Step1: Recall parallel lines definition

Parallel lines are lines in a plane that do not intersect. In Graph 1, the two lines have the same direction and will never meet.

Graph 2

• Step1: Recall parallel and perpendicular lines properties

Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals. The two lines in Graph 2 intersect at an angle that is not \(90^{\circ}\) and do not have the same slope.

Graph 3

• Step1: Recall parallel and perpendicular lines properties

The two lines in Graph 3 intersect at an angle that is not \(90^{\circ}\) and do not have the same slope.

Graph 4

• Step1: Recall perpendicular lines definition

Perpendicular lines intersect at a right - angle (\(90^{\circ}\)). In Graph 4, the two lines intersect at a \(90^{\circ}\) angle.

Answer:

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