Question

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

Explanation:

Graph 1

• Step1: Check parallel lines definition

Parallel lines are lines in a plane that do not intersect. In Graph 1, the two lines are horizontal and do not intersect.

Graph 2

• Step1: Check parallel lines definition

Parallel lines have the same slope. Visually, the two lines in Graph 2 are non - intersecting and have the same "steepness" (if we consider them as linear functions in a coordinate system, they would have the same slope).

Graph 3

• Step1: Check intersection

The two lines in Graph 3 intersect at a non - right angle. Since they intersect and the angle between them is not \(90^{\circ}\), they are neither parallel nor perpendicular.

Graph 4

• Step1: Check 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: Parallel; Graph 3: Neither; Graph 4: Perpendicular