## Thomas' Calculus 13th Edition

$x=3+t,y=t-4, z=t-1$
As we know the parametric equations of a straight line for a vector $v=v_1i+v_2j+v_3k$ passing through a point $P(a,b,c)$ is given by $x=a+t v_1,y=b+t v_2; z=c+t v_3$ Since, we have $P(-3,-4,-1)$ and $v=\lt 1, 1, 1 \gt$ our parametric equations are: $x=3+t,y=t-4, z=t-1$