[tex]\begin{gathered} \text{Two lines are perpendicular when:} \\ \text{slope}1\cdot\text{ slope2 = -1} \\ \text{Line 1} \\ 2x-y=5 \\ y=2x-5 \\ \text{slope1 =2} \\ \text{slope}2=\frac{-1}{slope1} \\ \text{slope}2=-\frac{1}{2} \\ \text{Line 2} \\ y=-\frac{1}{2}x+b \\ P(6,-1) \\ -1=-\frac{1}{2}\cdot(6)+b \\ -1=-3+b \\ b=-1+3 \\ b=2 \\ y=-\frac{1}{2}x+2 \\ \text{The equation of the line is }y=-\frac{1}{2}x+2 \end{gathered}[/tex]
