Answer
$x=4-3t,y=-1+2t,z= 2+3t$
Work Step by Step
Given: $A(4,-1,2), B(1,1,5)$
The direction of the vectors is $\lt-3,2,3 \gt$
Formula for a line $r=r_{0}+tv$
where $r_{0}$ is the starting point vector and $v$ is the direction vector.
$r=\lt 4,-1,2\gt+t \lt -3,2,3\gt$
Therefore, the parametric equations of the line are:
$x=4-3t,y=-1+2t,z= 2+3t$