Find the equation of the plane that passes through the point $(0,3,-1)$ and is parallel to the plane $4x-y+3z=8$.

Step-by-step solution

1. Step 1: The given plane has normal vector $\mathbf{n}=(4,-1,3)$; the required plane must have the same normal.
2. Step 2: Write the plane equation in point‑normal form $4(x-0)-1(y-3)+3(z+1)=0$.
3. Step 3: Simplify: $4x-y+3z-3-3=0$, so $4x-y+3z=6$.
4. Step 4: Re‑arrange to standard form: $4x-y+3z=-6$ by moving constants to the right side. (Alternatively, compute $D$ directly: $4(0)-1(3)+3(-1)=-6$.)

Concept tested: Plane through point parallel to given plane

Published 10 October 2026 · How this solution was prepared and checked