Answer
$$y=\dfrac{1}{3}x+\dfrac{5}{3}$$
Work Step by Step
Recall:
(1) Parallel lines have the same or equal slopes.
(2) Perpendicular lines have slopes whose product is $-1$.
(3) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ is the slope and $b$ is the $y$-intercept.
The line is perpendicular to $3x+y=1$, whose slope is $-3$.
This means that the slope of the line we are looking for is the negative reciprocal of $-3$, which is $\frac{1}{3}$.
Thus, the tentative equation of the line is:
$$y=\frac{1}{3}x+b$$
Substitute $-2$ to $x$ and $1$ to $y$ to obtain:
\begin{align*}
y&=\frac{1}{3}x+b\\\\
1&=\frac{1}{3}(-2)+b\\\\
1&=\frac{-2}{3}+b\\\\
1+\frac{2}{3}&=b\\\\
\frac{5}{3}&=b
\end{align*}
Thus, the equation of the line is:
$$y=\dfrac{1}{3}x+\dfrac{5}{3}$$
