The second choice, y+1=6/11(x+4), is correct.
We first find the slope using the formula
m=(y₂-y₁)/(x₂-x₁)
Using our points, this gives us
m=(-1-5)/(-4-7) = -6/-11 = 6/11
Point-slope form is
y-y₁=m(x-x₁)
Using the first point, we would have
y-5=6/11(x-7)
Using the second point, we would have
y--1=6/11(x--4)
y+1=6/11(x+4)
