Answer
$\textbf{r} = \langle 0,0,1\rangle + t\langle0,1,0 \rangle$
Work Step by Step
Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$
$\textbf{r}_0 = \langle 0,0,1\rangle$
Since the line is parallel to the $y$-axis, the orientation of $\textbf{v}$ must be parallel to the $y$-axis. In other words, we can use the unit vector $\textbf{j}$ as our $\textbf{v}$. Thus, $\textbf{v} = \textbf{j}=\langle 0,1,0 \rangle $
$\textbf{r} = \langle 0,0,1\rangle + t\langle0,1,0 \rangle$
