Passes through (4,-2) and m = 0.
we know that
the equation of the line in point slope form is equal to
y-y1=m(x-x1)
In this problem we have
m=0
and
(x1,y1)=(4,-2)
substitute
y+2=0(x-4)-------> equation in point slope form
y+2=0
y=-2
Part 2
passes through (-1,-7) and (1,3)
we know that
the equation of the line in point slope form is equal to
y-y1=m(x-x1)
step 1
Find the slope m
m=(3+7)/(1+1)
m=10/2
m=5
step 2
Find the equation of the line
we have
m=5
take the point (-1,-7)
substitute
y+7=5(x+1) -----> equation in point slope form
If you take the point (1,3)
the equation is
y-3=5(x-1)