Answer
$$x = - 4t + 1,{\text{ }}y = 4t - 6,{\text{ }}z = - 3t + 8$$
Work Step by Step
$$\eqalign{
& P\underbrace {\left( {1, - 6,8} \right)}_{{x_1},{y_1},{z_1}},{\text{ }}Q\underbrace {\left( { - 3, - 2,5} \right)}_{{x_2},{y_2},{z_2}} \cr
& {\text{Find }}{\bf{v}} \cr
& {\bf{v}} = \left\langle {{x_2} - {x_1},{y_2} - {y_1},{z_2} - {z_1}} \right\rangle \cr
& {\bf{v}} = \left\langle { - 3 - 1, - 2 + 6,5 - 8} \right\rangle \cr
& {\bf{v}} = \left\langle { - 4,4, - 3} \right\rangle \cr
& {\text{Then, }} \cr
& {\bf{r}}\left( t \right) = {\bf{v}}t + \left\langle {{x_1},{y_1},{z_1}} \right\rangle \cr
& {\bf{r}}\left( t \right) = \left\langle { - 4,4, - 3} \right\rangle t + \left\langle {1, - 6,8} \right\rangle \cr
& {\bf{r}}\left( t \right) = \left\langle { - 4t + 1,4t - 6, - 3t + 8} \right\rangle \cr
& x = - 4t + 1,{\text{ }}y = 4t - 6,{\text{ }}z = - 3t + 8 \cr} $$
