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 Lines Definition

Parallel lines are lines in a plane that never meet and are always the same distance apart.

Step2: Analyze Graph 1

The two lines in Graph 1 are horizontal, so they have the same slope (slope of horizontal line is \(0\)) and never intersect. So they are parallel.

Graph 2:

Step1: Recall Perpendicular Lines Definition

Perpendicular lines are lines that intersect at a right angle (\(90^\circ\)).

Step2: Analyze Graph 2

One line is vertical (undefined slope) and one is horizontal (slope \(0\)). A vertical and a horizontal line intersect at \(90^\circ\), so they are perpendicular.

Graph 3:

Step1: Recall Parallel Lines Definition

Parallel lines have the same slope (direction).

Step2: Analyze Graph 3

The two lines in Graph 3 have the same direction (both rising with similar steepness), so they have the same slope. Thus, they are parallel.

Graph 4:

Step1: Recall Perpendicular and Parallel Conditions

Parallel lines have same slope, perpendicular have slopes that are negative reciprocals.

Step2: Analyze Graph 4

The two lines intersect but do not form a right angle (their slopes are not negative reciprocals, and they are not parallel). So they are neither.

Answer:

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