From the slope formula
(5-1)/(-3-1). slope = -1.
Finding the y intercept (b in this case)
y = -x + b
We plug in one of the points we have to solve for b (I use (1,1) you can use (-3,5) if you want)
y = -x + b
1 = -(1) + b
1 = -1 + b
2 = b
So now we have our formula
y = -x + 2