if m is not given, we can find it if two points are given in the following way.
let the points given be (x1,y1) and (x2,y2), then
m = (y2 - y1)/(x2 - x1)
after finding the value for m, we can use it and any one set of points to find b, by either plugging in all the values into y = mx + b (at this time, b will be the only thing unknown) or plugging the values into the point-slope form and solving for y.
point-slope form: y - y1 = m(x - x1)
so now let's do your problem.
the points given are (1,-3) and (-1,1)
=> m = (y2 - y1)/(x2 - x1) = (1 - (-3))/(-1 - 1) = 4/-2 = -2
using (x1,y1) = (-1,1), we have by the point-slope form:
y - y1 = m(x - x1)
=> y - 1 = -2(x - (-1)) = -2x - 2
=> y = -2x - 1