Answer
$x=2-2t, y=-4+t, z=7-2t$
Work Step by Step
Step 1. Identify the given points: $P(2,-4,7)$ and $Q(0,-3,5)$
Step 2. Form a vector using the two points $\vec v=\vec{PQ}=\langle (0-2),(-3+4),(5-7) \rangle=\langle -2,1,-2\rangle$
Step 3. The general parametric equation of a line passing point $P(x_0,y_0,z_0)$ and parallel to vector $\vec u=\langle a,b,c, \rangle$ is given by $x=x_0+at, y=y_0+bt, z=z_0+ct$
Step 4. Use the above results to write the line equations as $x=2-2t, y=-4+t, z=7-2t$
