Step 1: Approach
Use the normal form of a line. The line has equal intercepts on both axes, so it is perpendicular to the direction at 45 degrees.
Step 2: Normal form
The perpendicular from the origin makes an angle $225^\circ$ with the x-axis, because both intercepts are negative. With $p=4$:
\[ x\cos225^\circ+y\sin225^\circ=4 \]
\[ -\frac{x}{\sqrt2}-\frac{y}{\sqrt2}=4\Rightarrow x+y+4\sqrt2=0 \]
Step 3: Check
The intercepts are $-4\sqrt2$ on both axes, equal and negative. So the answer is (B).
Final Answer:
The line is $x+y+4\sqrt{2}=0$, option (B).
\[ \boxed{x+y+4\sqrt{2}=0} \]