First thing to do is find the vector associated with the line passing through the two points spoken.
A = (2,-1,3) = (x1,y1,z1)
B = (-1,4,0)
AB = < b1-a1, b2-a2, b3-a3>
AB = < -1-2, 4-(-1), 0-3>
AB = < -3, 5, -3> = < a,b,c>
Now as this vector passes through say Point A, this line can parameterized by the equations:
x = x1 + at
y = y1 + bt
z = z1 + ct
x = 2 - 3t
y = -1 + 5t
z = 3 - 3t
Feel free to correct me if I misspoke at any point. Hope this was helpful.
