Chapter 9 - Section 9.6 - Equations of Lines and Planes - 9.6 Exercises - Page 669: 9

$x=1+t, y= -3+4t, z=2-3t$

A vector determined by the two given points is $\textbf{v}=\,<2-1,1-(-3),-1-2>=\,<1,4,-3>$ Using $\textbf{v}$ and the point (1,-3,2), we find that the parametric equations are $x=1+1t=1+t$ $y= -3+4t$ $z=2+(-3t)=2-3t$