Answer
$y=-\dfrac{5}{3}x+4$
Work Step by Step
Step 1. Find the slope of the line.
The line $y=\frac{3}{5}x-1$ has a slope of $m=\frac{3}{5}$.
The slope of the line perpendicular to this line is the negative reciprocal of $\frac{3}{5}$. Thus, the slope of the line we are looking for is $-\frac{5}{3}$.
Step 2. Find the equation of the line.
Using the point-slope form with $m=-\frac{5}{3}$ and the point $(3, -1)$, the equation of the line is:
$$\begin{align*}
y-(-1)&=-\frac{5}{3}(x-3)\\
y+1&=-\frac{5}{3}x+5)\\
y&=-\frac{5}{3}x+5-1\\
y&=-\frac{5}{3}x+4\\
\end{align*}$$
