Answer
$x(t)=-2+13t,y(t)=18-22t,z(t)=31+17t$, for $0\leq t \leq 1$
Work Step by Step
The vector equation of a line segment from $r_0$ to $r_1$ is:
$r(t)=(1-t)r_0+tr_1$, for $0\leq t \leq 1$
$r(t)=(1-t)\lt-2,18,31\gt+t\lt11,-4,48\gt$
$r(t)=\lt-2+2t,18-18t,31-31t\gt+\lt11t,-4t,48t\gt$
$r(t)=\lt-2+13t,18-22t,31+17t\gt$
Hence, the parametric equations are:
$x(t)=-2+13t,y(t)=18-22t,z(t)=31+17t$, for $0\leq t \leq 1$
