Final answer:
Line QR and line ST are neither parallel nor perpendicular because their slopes, -3/2 for QR and 2/3 for ST, are neither equal nor negative reciprocals of each other.
Step-by-step explanation:
To determine whether line QR and line ST are parallel, perpendicular, or neither, we must find the slopes of each line. If two lines are parallel, their slopes are equal. If they are perpendicular, the product of their slopes is -1. The slope of a line through two points, (x1,y1) and (x2,y2), is given by m = (y2 - y1) / (x2 - x1).
For line QR, with points Q(-6, 11) and R(2, -1):
mQR = (-1 - 11) / (2 - (-6)) = -12 / 8 = -3/2
For line ST, with points S(-4, 8) and T(-1, 10):
mST = (10 - 8) / (-1 - (-4)) = 2 / 3
Since the slopes are neither equal nor negative reciprocals of one another, the lines QR and ST are neither parallel nor perpendicular.