Final answer:
After calculating the slopes of the two lines, we determine they are neither parallel nor perpendicular. The first line's slope is 1/4 and the second line's slope is 2/9. Their slopes are different, and the product of the slopes is not -1.
Step-by-step explanation:
The question asks whether two lines, based on given points, are parallel, perpendicular, or neither. To determine this, we need to find the slopes of the lines. The slope is calculated by the change in y divided by the change in x (rise over run).
For the first line passing through points (-8, 1) and (4, 4), the slope (m1) is:
m1 = (4 - 1) / (4 - (-8)) = 3 / 12 = 1/4
For the second line passing through points (-9, -7) and (9, -3), the slope (m2) is:
m2 = (-3 + 7) / (9 - (-9)) = 4 / 18 = 2/9
Since the slopes of the two lines are different, they are not parallel. For two lines to be perpendicular, the product of their slopes must be -1. In this case:
m1 * m2 = (1/4) * (2/9) = 2/36 = 1/18, which is not equal to -1. Therefore, the lines are neither parallel nor perpendicular.