Q. I need a find a system of linear equations with three unknown variables whose solutions are the points on the line through (1,1,1) and (3,5,0).

$ \frac{x-1}{2} = \frac{y-1}{4} = \frac{z-1}{-1}$
and I set them equal to t that is an arbitrary constant.

Then $ x = 2t + 1, y = 4t + 1 , z = -t + 1 $ becomes the solutions of the linear equation systems?

Is it correct? From here I know how to do it. Just wanted to make sure the intro solution was correct.
 Please let me know! Thanks!