What is an equation of the line that is perpendicular to the line whose equation is y=(3/5)x - 2...

and that passes through the point (3,-6)

Rule 1: A perpendicular line has a reciprocal gradient to the one it passes through.
This in mind, we know that the gradient of our unknown lines has a gradient of -5/3.

Now, we know that the equation of a straight line is y=mx+c
We have been given an x and y value, and we know the gradient, so all we have to do is input these values for x and y, find c via rearranging.
y=mx+c

-6=(-5/3)*3+c -6=-15/3+c -6=-5+c c=-6+5=-1

therefore the equation of our second line is y=(-5/3x)-1

y + 6 = -5/3*(x - 3)

y = -5x/3 - 1