line q has the equation 5 y – 3 x = 30 . 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 . )
"5 y - 3 x = 30 and so y = 3 x / 5 + 6 when x = 0 , then y = 6 . when y = 0 , then x = - 10 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 10 , 0 ) , 0 = - 5 ( - 10 ) / 3 + c the y - intercept is c = - 50 / 3 < - 16 . thus the perpendicular line s can have y - intercepts from - 16 up to 5 . the number of possible lines is 16 + 5 + 1 = 22 the answer is a ."
add(subtract(divide(30, 5), const_2), add(divide(30, 3), divide(30, 5)))