Chapter 11 - Section 11.5 - Lines and Planes in Space - Exercises - Page 630: 1

$x=3+t,y=t-4, z=t-1$

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 $P(-3,-4,-1)$ and $v=\lt 1, 1, 1 \gt$ Thus, we get the parametric equations: $x=3+t,y=t-4, z=t-1$