I'll mark

write the equation of a line that is perpendicular to the given line and that passes through the given point.

y-2= 7/3(x+5) ; (-5, 2)

a: y+2= -3/7 (x-5)
b: y-5= -3/7(x+2)
c: y-2= -3/7(x+5)
d: y+2= 3/7(x-5)

a:

Equation of a line that passses through (x1,y1) and has a slope of m is
y-y1=m(x-x1)

perpendicular lines have slopes that mulitply to get -1
given
y-2=7/3(x+5)
slope is 7/3

perpendicular
7/3 times slope=-1
times 3/7 both sides
slope=-3/7

given point is (-5,2)

y-2=-3/7(x-(-5))
y-2=-3/7(x+5)

C is answer