Equation of Line Geometry Question

What is an equation of the line that is perpendicular to the line whose equation is y=3/5x-2 and that passes through the point (3,-6)?

(1) y = 5/3x - 11
(2) y = -5/3x + 11
(3) y = -5/3x - 1
(4) y = 5/3x +1


I understand the first part of how to get the perpendicular part so i know I can eliminate (1) and (4) but I don't understand How you find out which one passes through that point. Do you have to plug in the coordinates? Thanks in advance.

You do have to plug the coordinates using the point-slope equation.

y + 6 = -5/3(x - 3)
y + 6 = -5/3x + 5
y = -5/3x - 1

m = 3/5 from y = 3/5x - 2

m = - 1/(3/5)
m = - 5/3

solving its slope intercept form

y = mx + b
- 6 = - 5/3(3) + b
- 6 = - 5 + b
- 6 + 5 = b
b = - 1

the equation of the line is, y = - 5/3x - 1 answer//

Answer is (3) y = -5/3x - 1