Answer
$\text{slope: }
\dfrac{7}{5}
,\\\\\text{$y$-intercept: }
0$
Work Step by Step
Using the properties of equality, the given equation, $
7x=5y
$, is equivalent to
\begin{array}{l}
5y=7x
\\\\
y=\dfrac{7}{5}x
\\\\
y=\dfrac{7}{5}x+0
.\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{7}{5}
,\\\\\text{$y$-intercept: }
0
.\end{array}