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

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