In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: line q has the equation 5 y 3 x = 60 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ' s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
c