For perpendicular lines m2 = -1/m1, i.e. the product of the two slopes equals -1.
x - 5y = 3
5y = x + 3
y = 1/5 x + 3/5 => slope = 1/5
m2 = -1/(1/5) = -5
Equation of a line containing point (-4, 6) with a slope of -5 is
y - 6 = -5(x - (-4))
y - 6 = -5(x + 4)
y - 6 = -5x - 20
5x + y = -20 + 6
5x + y = -14
