Question

what is the relationship between the slope of line q and the slope of line p?
the slope of line q is half the slope of line p.
the slope of line q is the opposite of the slope of line p.
the slope of line q is the reciprocal of the slope of line p.
the slope of line q is the opposite reciprocal of the slope of line p.

Explanation:

Step1: Recall slope - perpendicular line relationship

If two lines are perpendicular, the product of their slopes is - 1. When the product of two non - zero numbers \(m_1\) and \(m_2\) is - 1, \(m_2=-\frac{1}{m_1}\), which means one slope is the opposite reciprocal of the other. Visually, line \(p\) and line \(q\) in the graph are perpendicular.

Answer:

The slope of line \(q\) is the opposite reciprocal of the slope of line \(p\).