Final answer:
The slope of line v is approximately -0.89, and the slope of line w, being perpendicular to line v, is the negative reciprocal, which is approximately -1.12, closest to Option 3: -1.2.
Step-by-step explanation:
The slope of line v can be calculated using the two given points (1, 11) and (10, 3). The slope (m) is found by the formula m = (y2 - y1) / (x2 - x1). For our points, this would be m = (3 - 11) / (10 - 1) = (-8) / (9), which simplifies to approximately -0.89.
A line that is perpendicular to another line has a slope that is the negative reciprocal of the original line's slope. Therefore, the slope of line w, which is perpendicular to line v, would be 1 / 0.89, which is approximately 1.12. However, due to the signs, it would actually be -1.12, which is closest to Option 3: -1.2.