Answer
$y+3=-\dfrac{1}{3}(x-1)$
Work Step by Step
Using the properties of equality, the given linear equation, $
3x-y=2
$ is equivalent to
\begin{array}{l}
-y=-3x+2
\\\\
y=3x-2
.\end{array}
Using $y=mx+b$ or the Slope-Intercept form where $m$ is the slope, then the slope of the given line is $
3
$. Since perpendicular lines have negative reciprocal slopes, then the needed linear equation has slope equal to $
-\dfrac{1}{3}
$. Since it also passes through the given point $(
1,-3
)$, then using $y-y_1=m(x-x_1)$ or the Point-Slope form where $m$ is the slope and $(x_1,y_1)$ is a point on the line, the equation of the needed line is
\begin{array}{l}
y-(-3)=-\dfrac{1}{3}(x-1)
\\\\
y+3=-\dfrac{1}{3}(x-1)
.\end{array}
