On the coordinate plane, a line passes through the point $( 4,1 )$ and is perpendicular to the vector $\vec { n } = ( 1,2 )$. Let the coordinates of the points where this line meets the $x$-axis and $y$-axis be $( a , 0 ) , ( 0 , b )$ respectively. Find the value of $a + b$. [3 points]