Give parametric equations for the line in 3 space

Question

Give parametric equations for the line in 3 space which goes through the point (1,2,3) and is parallel to the line given by the symmetric equations:

(x-1)/-1 = (y-2)/3 = (z-2)/1

So, based off those symmetric equations I used the definition of a vector equation which is:

$<x,y,z>$ = <$x_0$, $y_0$, $z_0$> + $t<a,b,c>$

By using that I thought it would be simple and I could use the parametric equations to get my answer:

$x=1-t$

$y=2-3t$

$z=2-t$

Was this question not as simple as I thought? Or is there something im missing with the relation of symmetric equations and parametric equations?

UPDATE: Using the hint, by setting everything equal to t I have my new answers as:

$x=1-t$

$y=3t+2$

$z=t+2$

Answer 1

Hint: Add "$=t$" to the end of your symmetric equations, then solve for each of $x$, $y$, and $z$. Your equation for $x$ looks good, but you'll find different equations for $y$ and $z$.

Answer 2

Using the hint from Austin C:

$x=1-t$

$y=3t+2$

$z=t+2$