Final answer:
Lines c and d are parallel because they both have the same slope of 6/7.
Step-by-step explanation:
The question asks whether line c and line d are parallel or perpendicular. To determine this, we need to compare their slopes. If the slopes are the same, the lines are parallel. If the product of their slopes is -1, the lines are perpendicular.
To find the slope of line c, we use the formula for slope, which is (change in y)/(change in x), also known as (y2 - y1)/(x2 - x1). For line c, which passes through points (9, 7) and (2, 1), the slope is (1 - 7) / (2 - 9) = -6 / -7 = 6/7.
Similarly, for line d, which passes through points (8, 8) and (1, 2), the slope is (2 - 8) / (1 - 8) = -6 / -7 = 6/7. Since the slopes are equal, lines c and d are parallel.