Answer
$2x-5y=-23$
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*}\require{cancel}
y_1&=
7
,\\x_1&=
6
,\\m&=
\dfrac{2}{5}
,\end{align*}
is
\begin{align*}\require{cancel}
y-7=\dfrac{2}{5}(x-6)
\end{align*}
In the form $Ax+By=C,$ the equation above is equivalent to
\begin{align*}
5(y-7)&=\left( \dfrac{2}{5}(x-6) \right)5
\\\\
5(y-7)&=2(x-6)
\\
5y-35&=2x-12
\\
-2x+5y&=-12+35
\\
-2x+5y&=23
\\
-1(-2x+5y)&=(23)(-1)
\\
2x-5y&=-23
\end{align*}
