Answer
$r=\lt 6+t,-5+3t,2-\frac{2}{3}t\gt $
and
$x=6+t,y=-5+3t,z=2-\frac{2}{3}t $
Work Step by Step
Equation of the line is given by $r=r_0+tv$
$r=\lt 6,-5,2\gt $ and $v=\lt 1,3,\frac{-2}{3}\gt $, so the equation is
$r=\lt 6,-5,2\gt +\lt t,3t,\frac{-2}{3}t\gt $
In order to get the parametric equations, we will take the sum.
$r=\lt 6+t,-5+3t,2-\frac{2}{3}t\gt $
and
$x=6+t,y=-5+3t,z=2-\frac{2}{3}t $
