Question

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

Explanation:

Graph 1

• Step1: Check for parallel (same slope) or perpendicular (slope product - 1)

The lines in Graph 1 intersect at an angle that is not \(90^{\circ}\) and do not have the same slope (parallel lines have the same slope).

Graph 2

• Step1: Check for perpendicular (slope product - 1)

In Graph 2, the lines intersect at \(90^{\circ}\). For two non - vertical lines \(y = m_1x + c_1\) and \(y=m_2x + c_2\), if they are perpendicular \(m_1\times m_2=- 1\). A horizontal line has a slope \(m_1 = 0\) and a vertical line has an undefined slope, but geometrically, horizontal and vertical lines are perpendicular.

Graph 3

• Step1: Check for parallel (same slope)

Parallel lines are lines in a plane that do not intersect. The lines in Graph 3 have the same direction (no intersection) which means they have the same slope (for non - vertical lines \(y = m_1x + c_1\) and \(y=m_2x + c_2\), \(m_1=m_2\) for parallel lines)

Graph 4

• Step1: Check for parallel (same slope) or perpendicular (slope product - 1)

The lines in Graph 4 intersect at an angle that is not \(90^{\circ}\) and do not have the same slope.

Answer:

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