Ответ:

Подставим координаты точек  [tex]\bf M(5;-3)\ ,\ \ N(8;3)[/tex]  в уравнение

 [tex]\bf ax+by=13[/tex]  и решим систему уравнений :

[tex]\left\{\begin{array}{l}\bf 5a-3b=13\\\bf 8a+3b=13\end{array}\right\ \ \left\{\begin{array}{l}\bf 5a-3b=13\\\bf 5a-3b=8a+3b\end{array}\right\ \ \left\{\begin{array}{l}\bf 5a-3b=13\\\bf 3a=-6b\end{array}\right\\\\\\\left\{\begin{array}{l}\bf 5a-3b=13\\\bf a=-2b\end{array}\right\ \ \left\{\begin{array}{l}\bf -10b-3b=13\\\bf a=-2b\end{array}\right\ \ \left\{\begin{array}{l}\bf -13b=13\\\bf a=-2b\end{array}\right[/tex]      

[tex]\left\{\begin{array}{l}\bf b=-1\\\bf a=2\end{array}\right\ \ \ \Rightarrow \ \ \ \bf 2x-y=13[/tex]