Answer
$x=3+4t; y=7-4t; z=-5$
Work Step by Step
The line passing through containing the point $P(p,q,r)$ and parallel to the normal vector $n=\lt a,b,c\gt$ is expressed by the parametric equations as follows:
$x=p+at; y=q+bt; z=r+ct$
Here, $t$ is any real number.
Now, the line passing through containing the point $P(3,7,-5)$ and parallel to the normal vector $n=\lt 4,-4,0 \gt $ is expressed by the parametric equations as follows:
$x=3+4t; y=7-4t; z=-5+0t$
or, $x=3+4t; y=7-4t; z=-5$
