Question

Which is the equation in slope-intercept form of the line that contains points A and C? 

x = -y -6
x + y = 6
y+ 4 = -1 (x+2)
y= -x -6

Answer 1

we have that

point C(-2,-4)
point A(-4,-2)

we know that
the equation of a line in the intercept form is
y=mx+b

Step 1
find slope m
m=(y2-y1)/(x2-x1)
m=(-2+4)/(-4+2)------> 2/-2-------> m=-1

Step 2
find the value of b
with m=-1 and point C(-2,-4)
-4=-1*(-2)+b--------> -4=2+b-------> b=-6

y=mx+b
y=-x-6

the answer is
y=-x-6