Answer
$x=1+2t, y=-4t, z=2t$
Work Step by Step
Step 1. Establish a vector along the line $\vec v=\vec {PQ}=\langle 3-1,-4-0,2-0 \rangle=\langle 2,-4,2 \rangle$
Step 2. The general parametric equations for a line passing point $P(x_0,y_0,z_0)$ and parallel to a vector $\langle a,b,c \rangle$ are $x=x_0+at, y=y_0+bt, z=z_0+ct$
Step 3. We can obtain the equations for this problem as: $x=1+2t, y=-4t, z=2t$
