Final answer:
The slope of line w, which is perpendicular to line v passing through the points (1, 12) and (10, 7), is 9/5.
Step-by-step explanation:
To find the slope of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. The slope of a line passing through points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1).
Using the given points (1, 12) and (10, 7), we can calculate the slope of line v: slope_v = (7 - 12) / (10 - 1) = -5/9. The slope of line w, which is perpendicular to line v, is the negative reciprocal of the slope_v. Therefore, the slope of line w is 9/5.