Explanation:
since we have only points as information, let's us the point-slope form as equation :
y - y1 = a(x - x1)
a being the slope, (x1, y1) is a point on the line.
the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another. the direction itself does not matter, but is is important to use for the x and y difference calculations the same direction.
from (1, -7) to (-1, 5) we see
x changes by -2 (from 1 to -1).
y changes by +12 (from -7 to 5).
the slope is
+12/-2 = -6
so, when using e.g. (1, -7), our equation is
y - -7 = -6(x - 1)
y + 7 = -6x + 6
we could transform this now easily into the point-intercept form
y = ax + b
y + 7 = -6x + 6
y = -6x - 1
so, pick the form of equation that you like.