Here think about your starting point, say it is P.

Start at (5,−2,3)(5,−2,3) then to get to Q, you must travel in the direction of Q which is given by Q−P=(2,−7,8)−(5,−2,3)=(−3,−5,5). Now, traveling this direction in any scaled value gives you a line determined by the following vector equation:

(5,−2,3)+t(−3,−5,5)

which you can write in parametric form:

x=5−3t, y=−2−3t, and z=3+5t

notice that all we did was just write it in a form that represents a formula for each point (x,y,z)(x,y,z).