Answer
$x=1-3t,y=2, z=3+7t$
Work Step by Step
The parametric equations of a straight line can be found by knowing the value of a vector such as $v=v_1i+v_2j+v_3k$ passing through a point $P(x_0,y_0,z_0)$ as follows:
$x=x_0+t v_1,y=y_0+t v_2; z=z_0+t v_3$
Here, we have the vector $v=\lt -3,0,7 \gt$ and $P=(1,2,3)$ .
Thus, we get the parametric equations:
$x=1+(-3)t,y=2+t(0), z=3+(7)t$
Hence, $x=1-3t,y=2, z=3+7t$
