geometry math problem

Question

Write an equation of the line passing through the point (5,1)  that is perpendicular to the line 5x+3y=15

Answer 1

5x + 3y = 15

3y = -5x + 15

y = (-5/3)x + 5

We have two options for solving.

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

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

y = (3/5)x - 2

orrrr...

1 = (3/5)(5) + b

1 = 3 + b

b = -2

y = (3/5)x - 2