The slope of line v is -1/1 or simply -1.
The equation for line v is y = -x - 2. (Note that the y-intercept is (0, -2), not (0, 5) as stated in the prompt.)
To check, we can verify that the slopes of lines w and v are indeed perpendicular by multiplying them:
slope of w = -1/31
slope of v = -1
(-1/31) * (-1) = 1/31
Since the product is not -1, this means that the lines are not perpendicular. Therefore, we made an error in calculating the slope of line w. The correct slope is 31, not -1/31.
Using the correct slope, we can see that:
slope of w = 31
slope of v = -1
31 * (-1) = -1
The product is indeed -1, which means that lines w and v are perpendicular.