Final answer:
To find the equation of a plane parallel to a given plane and passing through a given point, we can use the point-normal form of the equation of a plane.
Step-by-step explanation:
To find an equation of the plane, we can start by finding the normal vector to the given plane. The normal vector of a plane is the coefficients of x, y, and z in the equation of the plane. So in this case, the normal vector of the plane 4x - y - z = 2 is (4,-1,-1).
Since the plane we're looking for is parallel to the given plane, it will have the same normal vector. Now we can use the point-normal form of the equation of a plane to find the equation. The point-normal form is given by (x-x_0)*a + (y-y_0)*b + (z-z_0)*c = 0, where (x_0, y_0, z_0) is a point on the plane and (a,b,c) is the normal vector.
Plugging in the values from the given point (4, -9, -6) and the normal vector (4,-1,-1), we get (x-4)*4 + (y-(-9))*(-1) + (z-(-6))*(-1) = 0. Simplifying this equation gives us 4x - y - z + 25 = 0. Therefore, the equation of the plane is 4x - y - z + 25 = 0.