Question

Select the equations that are parallel and perpendicular to y = -3x - 1 and that pass through the point (3, 1).

parallel: y = -3x + 6
perpendicular: y = one over three x + two and two thirds

parallel: y = -3x + 10
perpendicular: y = one over three x

parallel: y = negative one over three x
perpendicular: y = -3x

parallel: y = one over three x + 1
perpendicular: y = 3x - 1

Answer 1

keep in mind that parallel lines will have the same slope as y = -3x-1
and perpendicular lines will have a NEGATIVE RECIPROCAL slopes of that

notice the slope of y = -3x-1 \(\large y={\color{brown}{ -3}}x-1
\begin{cases}
parallel\\
\hline\\
slope\to {\color{brown}{ -3}}\\
perpendicular\\
\hline\\
{\color{brown}{ -3}}\quad negative\to {\color{brown}{ +3}}\quad reciprocal\to \frac{1}{{\color{brown}{ +3}}}
\end{cases}\)