step 1
Find the slope
we need two points
we take
(-4,2) and (-2,0)
m=(0-2)/(-2+4)
m=-2/2
m=-1
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=-1
point (-2,0)
substitute
0=(-1)(-2)+b
0=2+b
b=-2
so
y=-x-2
step 3
Verify option A, C and option D (because the slope is -1)
option A
y-5=-(x+3)
isolate the variable y
y-5=-x-3
y=-x+2 -------> is not the solution
option C
y-3=-(x+5)
y-3=-x-5
y=-x-2 ------> is the solution
therefore
answer is the option C