What is the value of k in this problem? Line 1: (-5, -2) and (0,0) Line 2: (1,6) and (k,7)?

If the lines are parallel, then their slopes are equal

2/5 = (7 - 6)/(k - 1)

2/5 = 1/(k - 1)

2(k - 1) = 5

2k - 2 = 5

2k = 7

k = 3.5

How are the lines related? Parallel? Perpendicular? Intersecting at a point?

UPDATE:
In order to be parallel the lines must have the same slope.

Remember:
slope = "rise" over "run"

As a formula, the slope between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
m = (0 - (-2)) / (0 - (-5))
m = 2/5


So you want the solve for the second line to be the same:
m' = 2/5 = (7 - 6) / (k - 1)
2/5 = 1/(k - 1)

Cross multiply:
2(k - 1) = 5
k - 1 = 5/2
k = 1 + 5/2
k = 2/2 + 5/2
k = 7/2

Answer:
k = 3½

To verify this, check the graph of the two lines below.