Rewriting the equation of the given line in slope-intercept form,
[tex]2x-3y=13\\\\2x-13=3y\\\\y=\frac{2}{3}x-\frac{13}{3}[/tex]
Thus, the slope of the given line is 2/3. Since perpendicular lines have slopes that are negative reciprocals of each other, we want to find the line with a slope of -3/2.
Substituting into point-slope form,
[tex]y-5=-\frac{3}{2}(x+6)\\\\y-5=-\frac{3}{2}x-9\\\\\boxed{y=-\frac{3}{2}x-4}[/tex]
