Answer
perpendicular
Work Step by Step
Using $y=mx+b$ where $m$ is the slope, the slope of the first equation,
\begin{array}{l}\require{cancel}
y=\dfrac{1}{3}x-7
\end{array}
is $m_1=
\dfrac{1}{3}
.$
Using $y=mx+b$ where $m$ is the slope, the slope of the second equation,
\begin{array}{l}\require{cancel}
y+3x=1
\\\\
y=-3x+1
\end{array}
is $m_2=
-3
.$
Since $m_1\cdot m_2=-1,$ then the given lines are $\text{
perpendicular
.}$
