Answer
$2x-3y=-15$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions,
\begin{align*}
y_1=5
,\\x_1=0
,\\m=\dfrac{2}{3}
,\end{align*}
is
\begin{align*}
y-5&=\dfrac{2}{3}(x-0)
\\\\
y-5&=\dfrac{2}{3}x
\end{align*}
In the form $Ax+By=C,$ where $A,$ $B,$ and $C$ are integers, the equation above is equivalent to
\begin{align*}
3(y-5)&=\left( \dfrac{2}{3}x \right)3
\\
3y-15&=2x
\\
-2x+3y&=15
\\
-1(-2x+3y)&=(15)(-1)
\\
2x-3y&=-15
\end{align*}
