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 for perpendicularity
• Perpendicular lines intersect at a right - angle (\(90^{\circ}\)). By visual inspection (assuming the grid is square - based), the lines in Graph 1 intersect at a right - angle.

Graph 2

• Step1: Check for parallelism
• Parallel lines never intersect and have the same slope. The lines in Graph 2 intersect, so they are not parallel.
• Step2: Check for perpendicularity
• They do not intersect at a right - angle.

Graph 3

• Step1: Check for parallelism
• The lines intersect, so they are not parallel.
• Step2: Check for perpendicularity
• They do not intersect at a right - angle.

Graph 4

• Step1: Check for parallelism
• Parallel lines never intersect. The lines in Graph 4 do not intersect and have the same "direction" (assuming the grid is uniform), so they are parallel.

Answer:

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