first, find the slope:
slope = rise / run = (y1 - y2) / (x1 - x2)
(5 - -1) / (1 - -2)
(5 + 1) / (1 + 2)
6 / 3
2
slope = 2
point-slope form:
y - y1 = m ( x - x1 )
pick one of the points (doesn't matter which one)
y - 5 = 2 ( x - 1)
y - 5 = 2x - 2
y = 2x + 3
put it in standard form:
-2x + y = 3