Answer
The equation of the perpendicular line is $y=-\frac{2}{5}x-\frac{11}{5}$
Work Step by Step
First, let's rearrange the line in the form y=mx+b:
$5x-2y=6$
$-2y=-5x+6$
$-2y/(-2)=(-5x+6)/(-2)$
$y=\frac{5}{2}x-3$
The slope of a perpendicular line is the negative inverse: $\frac{5}{2} \rightarrow -\frac{2}{5}$
Now that we have the slope and a point, we can find the equation of the perpendicular line by first finding the y-intercept (b):
$-3=-\frac{2}{5}(2)+b$
$-3=-\frac{4}{5}+b$
$-3+\frac{4}{5}=-\frac{4}{5}+b+\frac{4}{5}$
$-\frac{15}{5}+\frac{4}{5}=b$
$b=-\frac{11}{5}$
So, the equation of the perpendicular line is $y=-\frac{2}{5}x-\frac{11}{5}$