Two lines are perpendicular if the product of their slopes is -1.
[tex]y=mx+b \perp y=2x-3 \\ \Downarrow \\
m \times 2=-1 \\
m=-\frac{1}{2} \\ \\
y=-\frac{1}{2}x+b \\
P(-6,5) \\
x=-6, \ y=5 \\
\Downarrow \\
5=-\frac{1}{2} \times (-6)+b \\
5=3+b \\
5-3=b \\
b=2 \\ \\
\boxed{y=-\frac{1}{2}x+2}[/tex]
