to 1.) You have three points: A(-1, -2), B(6, -5), C(-10, 2).
If the slope between A and B is the same as the slope between B and C, then the three points lie on a straight line:
s means slope:
Both slopes are not equal therefore the three points don't lie on a straight line.
to 2.) You have 3 points: P(x, 3), Q(4, 1) and B(-5, -6)
a) Calculate the slope between Q and B:
. Thus the perpendicular direction is: -9/7 (have a look at topsquark's post!)
The slope between P and Q should be equal to this perpendicular slope:
. Solve for x.
(I've got x = 22/9)