Final answer:
To find an equation of the plane that passes through a given point and is parallel to a given plane, we can use the normal vector of the given plane to construct the equation.
Step-by-step explanation:
To find an equation of the plane that passes through the point (1, -5, -2) and is parallel to the plane 8x - y - z = 9, we need to find the normal vector of the given plane and use it to construct the equation of the parallel plane.
The normal vector of the given plane is (8, -1, -1) because the coefficients of x, y, and z in the equation of the plane represent the components of the normal vector. Since the parallel plane will have the same normal vector, we can use it to construct the equation.
Therefore, the equation of the plane that passes through the point (1, -5, -2) and is parallel to the plane 8x - y - z = 9 is 8(x - 1) - (y + 5) - (z + 2) = 0, which simplifies to 8x - y - z = 1.