Question

try again
one of your answers is incorrect.
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

Two lines are parallel if they have the same slope and never meet. In Graph 1, the two lines are vertical and will never intersect.

Graph 2

Two lines are perpendicular if the product of their slopes is - 1. In Graph 2, one line is horizontal (slope \(m_1 = 0\)) and the other is vertical (undefined slope in the traditional \(y=mx + b\) sense, but geometrically, a horizontal and vertical line form a \(90^{\circ}\) angle).

Graph 3

Let's assume the slopes of the two lines. If one line has a slope \(m_1\) and the other has a slope \(m_2\), for perpendicular lines \(m_1\times m_2=-1\). For parallel lines \(m_1 = m_2\). The two lines in Graph 3 have slopes \(m_1\) and \(m_2\) such that \(m_1\times m_2=- 1\) (one has a positive slope and the other has a negative slope with magnitudes that multiply to 1 when considering the rise - over - run).

Graph 4

The two lines in Graph 4 have different slopes (they are not parallel) and the product of their slopes is not - 1 (they are not perpendicular).

Answer:

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