Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 5 = - 3(x + 2) ← is in point- slope form
with slope m = - 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
and (a, b) = (6, - 1), hence
y - (- 1) = [tex]\frac{1}{3}[/tex](x - 6), that is
y + 1 = [tex]\frac{1}{3}[/tex](x - 6) → C
