Final answer:
The slope of line u is -6/7, and as line v is perpendicular to line u, the slope of line v is the negative reciprocal of line u's slope, which is 7/6.
Step-by-step explanation:
The slope of line u passing through the points (8, 4) and (1, 10) can be calculated using the slope formula, which is (y2 - y1) / (x2 - x1). So, the slope (m) of line u is (10 - 4) / (1 - 8) = 6 / (-7) = -6/7. Since line v is perpendicular to line u, its slope is the negative reciprocal of line u's slope. Therefore, the slope of line v is 7/6.