To find a line perpendicular to the original line, we must set the new slope as the negative reciprocal of the original slope, 2/5.
So the slope of the perpendicular line is -5/2
Now using the point slope form, we have the slope -5/2 and (3,6)
[tex]y- 6 = \frac{-5}{2}(x-3)\\y-6 =\frac{-5}{2} x + \frac{15}{2} \\y = \frac{-5}{2} x + \frac{15}{2} + 6\\y= \frac{-5}{2} x + \frac{15}{2} + \frac{12}{2} \\y = \frac{-5}{2}x +\frac{27}{2}[/tex]
Hope that helps!
