Find the equation of the line obtained by the rotation of the line x + y − 4 = 0 by pi/4
$\displaystyle x+y-4=0\Rightarrow\ y=-x+4$
which means the line has an angle of $\displaystyle -\frac{\pi}{4}$
relative to the positive side of the x-axis.
However, it does not go through the origin as $\displaystyle (0,4)$ is on the line.
The rotated line can pass through the origin, if we write the rotated line as $\displaystyle y=mx+c$, finding "m" and setting $\displaystyle c=0$
Is that what you are looking for ?