The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:
slope = (y2 - y1)/(x2 - x1)
Using the coordinates of the two given points, we have:
slope = (-12 - 3)/(4 - (-2))
slope = (-15)/(6)
slope = -5/2
Therefore, the slope of the line that passes through (-2, 3) and (4, -12) is -5/2.