Answer
$y=-\dfrac{2}{5}x-\dfrac{7}{5}$
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 parallel to $y=\frac{2}{5}x-3$ so its slope is also $\frac{2}{5}$. Thus, the tentative equation of the line is:
$$y=\frac{2}{5}x+b$$
Substitute $1$ to $x$ and $-1$ to $y$ to obtain:
\begin{align*}
y&=\frac{2}{5}x+b\\\\
-1&=\frac{2}{5}(1)+b\\\\
-1&=\frac{2}{5}+b\\\\
-1-\frac{2}{5}&=b\\\\
-\frac{7}{5}&=b
\end{align*}
Thus, the equation of the line is:
$$y=-\dfrac{2}{5}x-\dfrac{7}{5}$$
