Line Q has the equation 5y – 3x = 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.)  Pick:
A) 35 B) 40 C) 45 D) 50 E) 55
5y - 3x = 60 and so y = 3x/5 + 12   When x = 0, then y = 12.   When y = 0, then x = -20   The slope is 3/5, so the slope of line S is -5/3.   Through the point (-20, 0), 0 = -5(-20)/3 + c   The y-intercept is c = -100/3 &lt; -33.   Thus the perpendicular line S can have y-intercepts from -33 up to 11.   The number of possible lines is   33 + 11 + 1= 
<gadget id="calculator">  33 + 11 + 1</gadget>
<output>45</output>
45   The answer is 45.
<result>C</result>
Line Q has the equation 5y – 3x = 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.)