Equation of plane containing a line that is parallel to another plane

Find an equation of a plane containing the line r= <-5,2,-1> + t<-1,8,-4> which is parallel to the plane -4x+1y+3z=14 in which the coefficient of x is -4.

Please show your work. Thanks!!

Note that in the equation of the plane that states that Ax + By + Cz = D, the normal vector to the plane can be written as n = Ai + Bj + Ck. Since the two planes are parallel, the normal vector to the equation of the plane we want is n = 4i + j + 3k and since the plane goes through the point (-5, 2, -1), we can write the equation of the plane as:

4(x + 5) + (y - 2) + 3(z + 1) = 0 since n dotted with the vector must equal 0 since they're perpendicular.

4x + 20 + y - 2 + 3z + 3 = 0

4x + y + 3z = -21