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:

Step1: Recall line - relationship definitions

Parallel lines never intersect and have the same slope. Perpendicular lines intersect at a 90 - degree angle and the product of their slopes is - 1.

Step2: Analyze Graph 1

The two lines in Graph 1 are vertical and do not intersect. They have the same slope (undefined). So they are parallel.

Step3: Analyze Graph 2

The two lines in Graph 2 intersect but not at a 90 - degree angle. So they are neither parallel nor perpendicular.

Step4: Analyze Graph 3

The two lines in Graph 3 are horizontal and do not intersect. They have the same slope (0). So they are parallel.

Step5: Analyze Graph 4

The two lines in Graph 4 intersect at a 90 - degree angle. So they are perpendicular.

Answer:

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