Lines a and b are perpendicular. If the slope of line a is 3, what is the slope of line b? A. 3 B. -3 C. 1/3 D. -1/3

Accepted Solution

Answer:[tex]\large\boxed{D.\ -\dfrac{1}{3}}[/tex]Step-by-step explanation:[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ ||\ k\iff m_2=m_1\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\-------------------\\\\\text{We have the slope of given line a:}\ m_1=3.\ \text{Therefore the slope of a line b}\\\text{perpendicular to a is: }\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{3}[/tex]