Answer
$\text{slope: }
\dfrac{2}{5}
,\\\\\text{$y$-intercept: }
\dfrac{8}{5}$
Work Step by Step
Using the properties of equality, the given equation, $
2x-5y=-8
$, is equivalent to
\begin{array}{l}
-5y=-2x-8
\\\\
y=\dfrac{-2}{-5}x-\dfrac{8}{-5}
\\\\
y=\dfrac{2}{5}x+\dfrac{8}{5}
.\end{array}
Using $y=mx+b$ where $m$ is the slope and $b$ is the $y$-intercept, then the equation above has the following characteristics:
\begin{array}{l}
\text{slope: }
\dfrac{2}{5}
,\\\\\text{$y$-intercept: }
\dfrac{8}{5}
.\end{array}