Question

for each graph, decide if the two lines are parallel, perpendicular, or neither.
graph 1
graph 2
graph 3
graph 4
parallel
perpendicular
neither
parallel
perpendicular
neither
parallel
perpendicular
neither
parallel
perpendicular
neither

Explanation:

Graph 1

• Step1: Analyze the slopes

The lines are not parallel (different slopes, not same direction) and not perpendicular (product of slopes not - 1).

Graph 2

• Step1: Analyze the slopes

The lines are not parallel (different slopes) and not perpendicular (product of slopes not - 1).

Graph 3

• Step1: Analyze the slopes

One line is vertical (undefined slope) and the other is horizontal (slope = 0). The product of an undefined slope (vertical line) and 0 (horizontal line) is not applicable in the traditional \(m_1\times m_2=-1\) formula, but by geometric definition (they form a right - angle), they are perpendicular.

Graph 4

• Step1: Analyze the slopes

The lines have the same direction (same slope), so they are parallel.

Answer:

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