Answer
$4x-5y=-6$
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=2
,\\x_1=1
,\\m=\dfrac{4}{5}
,\end{align*}
is
\begin{align*}
y-2&=\dfrac{4}{5}(x-1)
\end{align*}
In the form $Ax+By=C,$ where $A,$ $B,$ and $C$ are integers, the equation above is equivalent to
\begin{align*}
5(y-2)&=\left(\dfrac{4}{5}(x-1)\right)5
\\
5y-10&=4(x-1)
\\
5y-10&=4x-4
\\
-4x+5y&=-4+10
\\
-4x+5y&=6
\\
-1(-4x+5y)&=(6)(-1)
\\
4x-5y&=-6
\end{align*}
