Question

Please help check my answer: describe the line passing through (-5,0,4) and (6,-3,2)::

=> l(t) = (-5+11t)i - (3t)j + (4-2t)k

Answer 1

yes.

the direction vector is pt1 - pt2 (or vice versa)
(6,-3,2) - (-5, 0, 4) = (11, -3, -2)
pick either point as the starting point:

P = (-5,0,4)+ t(11,-3,-2)

which is your version.
we could also do
P= (6,-3,2)+ t(11,-3,-2)

or
P= (6,-3,2)+ t(-11,3,2) (changed the signs of the direction vector)