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: Recall parallel/perpendicular rules

Parallel lines never meet, perpendicular lines form \(90^\circ\) angles.

Step2: Analyze Graph 1

The two lines intersect but don't form right angles. So, neither.

Graph 2:

Step1: Recall parallel/perpendicular rules

Parallel lines are equidistant, perpendicular form \(90^\circ\).

Step2: Analyze Graph 2

Lines intersect, no right angles, not parallel. So, neither.

Graph 3:

Step1: Recall perpendicular rule

Perpendicular lines form \(90^\circ\) (like vertical and horizontal).

Step2: Analyze Graph 3

One line is vertical, one horizontal—they form right angles. So, perpendicular.

Graph 4:

Step1: Recall parallel rule

Parallel lines have same slope (never meet, equidistant).

Step2: Analyze Graph 4

Two lines run in same direction, never meet. So, parallel.

Answer:

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