Hello, Craka!

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

Thus:

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 azillionpossible 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 . . .