Linear Algebra Lines vs. Vectors

Hi, I'm new to the forum, and to linear algebra. Not having much fun with that latter, I'm afraid. So I hope that this helps me understand the concepts that it deals with.

I guess I'll start with a question, try to work my way through it, and hopefully get it right, but if not, please correct me, and tell me where I went wrong and why.

Find the equation of the line parallel to v=(5,-2,1) passing through the point (1,6,2), and determine whether the point (5,4,3) is on this line.

I think that the equation of the line would be x=(1,6,2) + t (5,-2,1), because this would mean that (1,6,2) is on the line, and that the line has a direction of (5,-2,1). I'm not exactly sure how to figure out if the point is on the line, or if I'm even going in the right direction with this problem...