Suppose the solution set of a certain system of equations can be described as $x_1 = 6t-4$, $x_2 = 1-4t$, $x_3 = 3t-4$, $x_4 = 4-t$, where $t$ is a free variable. Use vectors to describe this solution set as a line in $\mathbb{R}^4$.

$L(t) =$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$ $+ t$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$.