There is an unavoidable problem with the equations of a line.Find the equations for line through points
The way I understand it this is what you do.
Get a directional vector between the two points
The parametrics would be: .
giving symmetric as: .
But it looks like I'm wrong . . . . WHO said you're wrong?
. . I wish textbook authors and math teachers would be own up to it.
There are a zillion possible forms of the equations of a line.
. . There is no "one right answer."
You used point and . . . and your answers are correct.
Suppose you used
You would have: . . . also correct.
, we can use a parallel vector: .
With point , we would have: .
You see, the variations are endless . . .