Answer
\begin{equation}
x_4\begin{pmatrix} 3 \\ 1 \\ -5 \\ 1 \end{pmatrix} +
\begin{pmatrix} 0 \\ 8 \\ 2 \\ 0 \end{pmatrix}
\end{equation}
where $x_4$ is a free variable.
Work Step by Step
We are given $x_1 = 3x_4$, $x_2 = 8 +x_4$, and $x_3 = 2-5x_4$
Thus, the line is given as, where $x_4$ is a free variable:
\begin{equation}
\begin{pmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{pmatrix} =
\begin{pmatrix} 3x_4 \\ 8 +x_4 \\ 2-5x_4 \\ x_4 \end{pmatrix} =
x_4\begin{pmatrix} 3 \\ 1 \\ -5 \\ 1 \end{pmatrix} +
\begin{pmatrix} 0 \\ 8 \\ 2 \\ 0 \end{pmatrix}
\end{equation}
