This is a question from my calculus 3 class.

"Find the parametric equation of the line through the origin that is parallel to the line given by x = 1, y = -1 + t, z = 2."

I'm not sure if I did this right, and frankly I'm still a little uneasy with parametric equations.

So to begin, I made a vector out of the parametric equations they gave me just for the heck of it:

v = <1, 1, 0>

In the given equations:

x_0 = 0

y_0 = -1

z_0 = 2

And so the parallel line would have:

x_0 = 0

y_0 = 0

z_0 = 0

Making the parallel parametric equations through the origin:

x = t

y = t

z = t

I don't feel this is correct, but my logic behind the answer is that if the line goes through the origin, then only the above parametric equations work right? Honestly I'm confused. I guess I need a bump in the right direction.