Answer
$$x+y+z=14.$$
Work Step by Step
Since the plane is parallel to the plane
$$ x+y+z=3$$
then its normal vector $ n $ is $\langle 1,1,1\rangle $
and, using the fact that the plane passes through $(4,1,9)$, the equation of the plane is given by
$$(x-4)+(y-1)+(z-9)=0\Longrightarrow x+y+z-14=0$$
Hence the equation is given by
$$x+y+z=14.$$
