Answer
$$y=\dfrac{5}{2}x+\dfrac{17}{2}$$
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 $y=-\frac{2}{5}x-4$ so its slope is the negative reciprocal of $-\frac{2}{5}$, which is $\frac{5}{2}$. Thus, the tentative equation of the line is:
$$y=\frac{5}{2}x+b$$
Substitute $-3$ to $x$ and $1$ to $y$ to obtain:
\begin{align*}
y&=\frac{5}{2}x+b\\\\
1&=\frac{5}{2}(-3)+b\\\\
1&=\frac{-15}{2}+b\\\\
1+\frac{15}{2}&=b\\\\
\frac{17}{2}&=b
\end{align*}
Thus, the equation of the line is:
$$y=\dfrac{5}{2}x+\dfrac{17}{2}$$
