Question

for each graph, decide if the two lines are parallel, perpendicular, or neither.
graph 1
graph 2
graph 3
parallel
parallel
parallel
parallel
perpendicular
perpendicular
perpendicular
perpendicular
neither
neither
neither
neither

Explanation:

Graph 1:

Step1: Recall line relationships

Parallel lines: same slope, never meet. Perpendicular: slopes multiply to -1 (or right angle).

Step2: Analyze Graph 1

One line horizontal (slope 0), one vertical (undefined slope). They form a right angle. So perpendicular.

Graph 2:

Step1: Recall parallel definition

Parallel lines have the same slope (direction) and never intersect.

Step2: Analyze Graph 2

The two lines have the same direction (slope) and are close, so they are parallel (they don't intersect and have same slope).

Graph 3:

Step1: Check slopes/direction

One line has a steeper slope, the other less steep. Different directions (slopes), not perpendicular (no right angle).

Step2: Conclude

So neither parallel nor perpendicular.

Graph 4 (assuming the last graph with two horizontal lines):

Step1: Recall horizontal lines

Horizontal lines have slope 0, same slope.

Step2: Analyze

Two horizontal lines: same slope, never meet. So parallel.

Answer:

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