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:

Graph 1:

Step1: Analyze line directions

One line is vertical (up - down), the other is horizontal (left - right).

Step2: Recall perpendicular definition

Perpendicular lines intersect at 90 - degree angles. Vertical and horizontal lines are perpendicular.
So Graph 1: Perpendicular.

Graph 2:

Step1: Analyze line directions

Both lines are vertical (same direction, parallel orientation).

Step2: Recall parallel definition

Parallel lines never intersect and have the same slope (vertical lines have undefined slope, same for both).
So Graph 2: Parallel.

Graph 3:

Step1: Analyze line directions

Both lines are horizontal (same direction, parallel orientation).

Step2: Recall parallel definition

Horizontal lines have slope 0, same for both, so they are parallel.
So Graph 3: Parallel.

Graph 4:

Step1: Analyze line directions

One line is slanting, the other is horizontal? Wait, no, one is slanting, the other is... Wait, looking at the graph, one line is sloped, the other is horizontal? Wait, no, the two lines: one is a slant, the other is a shallow slant? Wait, no, let's check slopes. If one line is not horizontal/vertical and the other is not perpendicular (product of slopes not - 1) and not same slope.

Step2: Check parallel/perpendicular

Parallel lines have same slope, perpendicular have slopes that multiply to - 1. These two lines: one is slanting, the other is... Wait, the lines are not parallel (different slopes) and not perpendicular (product of slopes not - 1). So Graph 4: Neither.

Answer:

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