Final answer:
By calculating the slopes of QR and ST, it is determined that the lines are neither parallel nor perpendicular because their slopes are not equal nor negative reciprocals of each other.
Step-by-step explanation:
To determine if the lines QR and ST are parallel, perpendicular, or neither, we first calculate the slopes of both lines. The slope is defined as the change in y divided by the change in x (rise over run).
For line QR, given points Q(-8,7) and R(-7,-2), the slope (mQR) is:
mQR = (7 - (-2)) / (-8 - (-7)) = 9 / -1 = -9
For line ST, given points S(-8,13) and T(-11,-2), the slope (mST) is:
mST = (13 - (-2)) / (-8 - (-11)) = 15 / 3 = 5
Since the slopes of QR and ST are not equal and neither the negative reciprocal of each other, lines QR and ST are neither parallel nor perpendicular.