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
• One line is horizontal (slope \(m_1 = 0\)), and the other is not horizontal (slope \(m_2

eq0\)).

• Parallel lines have equal slopes (\(m_1 = m_2\)), and perpendicular lines have \(m_1\times m_2=- 1\). Since \(m_1 = 0\) and \(m_2

eq0\), \(m_1
eq m_2\) and \(m_1\times m_2 = 0
eq - 1\).

Graph 2

• Step1: Analyze the intersection angle
• The lines intersect at an angle that is not \(90^{\circ}\) (parallel lines do not intersect in a plane, and perpendicular lines intersect at \(90^{\circ}\)).

Graph 3

• Step1: Check the direction
• The two lines are vertical (parallel lines are lines that never intersect and have the same "direction"). Vertical lines are parallel to each other.

Graph 4

• Step1: Check the direction
• The two lines are horizontal (parallel lines are lines that never intersect and have the same "direction"). Horizontal lines are parallel to each other.

Answer:

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