[tex](2, -5) , \ \ \ x - 5y = - 8 \\ \\ x - 5y = - 8 \ subtract \ (-x )\ from \ each \ side \\ \\ -5y = - x -8 \ divide \ each \ term \ by \ (-5) \\ \\ y = \frac{1} {5}x + \frac{ 8}{5}\\ \\ The \ slope \ is : \ m _{1} = \frac{1}{5}[/tex]
[tex]If \ m_{1} \ and \ m _{2} \ are \ the \ gradients \ of \ two \ perpendicular \\ \\ lines \ we \ have : \\ m _{1}*m _{2} = -1 \\\\\frac{1}{5}\cdot m_{2}=-1 \ \ / \cdot 5\\\\m_{2}=-5[/tex]
[tex]Now \ your \ equation \ of \ line \ passing \ through \ (2,-5) would \ be: \\ \\ y=m_{2}\cdot x+b \\ \\-5=(-5) \cdot 2 + b \\ \\ -5= -10+b\\ \\ b=-5+10=5\\\\ y = -5x +5[/tex]
