Find k so that the line containing the points (-3,k) and (6,6) is parallel to the line containing the points (5,5) and (1,-2)

The slope between the points (5,5) and (1, -2) is 7/4
A line parallel to to that would also be 7/4 (m = 7/4)

Use the Point-Slope formula to find k:
Let (6,6) = (x, y) and let (-3, k) = (x1, y1)
y - y1 = m(x - x1)
6 - k  = (7/4)(-3 - 6)
6 - k = (7/4)(-9)
6 - k = -63/4
6 + 63/4 = k
24/4 + 63/4 = k
87/4 = k