Write vector and Cartesian equations without dividing by zero

The point is $(7,2,-4)$ and direction $(1,-3,1)$. A vector equation is

$\mathbf r=(7,2,-4)+\lambda(1,-3,1),\quad\lambda\in\mathbb R.$

Eliminating the parameter gives

$x-7=\frac{y-2}{-3}=z+4.$

The source difference $(2,-2,1)-(0,4,9)=(2,-6,-8)=-2(-1,3,4)$ gives direction $(-1,3,4)$. Thus

$\mathbf r=(2,-2,1)+\lambda(-1,3,4),\quad\lambda\in\mathbb R.$

The Cartesian equation is

$2-x=\frac{y+2}{3}=\frac{z-1}{4}.$

Parameter 2 recovers $(0,4,9)$.

Rewrite the given line as $\mathbf r=(2,0,5)+p(-1,1,0)$. The required line passes through $(7,0,0)$ with that direction:

$\mathbf r=(7,0,0)+\lambda(-1,1,0),\quad\lambda\in\mathbb R.$

Its Cartesian description is

$7-x=y,\qquad z=0.$

A zero direction component means a constant coordinate, not division byzero.