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: Recall parallel lines definition

Parallel lines never intersect and have same slope.

Step2: Analyze Graph 1 lines

The two lines in Graph 1 do not intersect and have same direction (slope), so they are parallel.

Graph 2

Step1: Recall non - parallel and non - perpendicular lines

Lines that are not parallel (intersect) and do not form \(90^{\circ}\) angle.

Step2: Analyze Graph 2 lines

The two lines in Graph 2 intersect but not at \(90^{\circ}\), so they are neither parallel nor perpendicular.

Graph 3

Step1: Recall non - parallel and non - perpendicular lines

Lines that are not parallel (intersect) and do not form \(90^{\circ}\) angle.

Step2: Analyze Graph 3 lines

The two lines in Graph 3 intersect but not at \(90^{\circ}\), so they are neither parallel nor perpendicular.

Graph 4

Step1: Recall perpendicular lines definition

Perpendicular lines intersect at \(90^{\circ}\).

Step2: Analyze Graph 4 lines

The two lines in Graph 4 intersect at \(90^{\circ}\), so they are perpendicular.

Answer:

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