Line Q has the equation 5y – 3x = 75. 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.)
Choose the correct choice from the following
A) 48	B) 52	C) 56	D) 60	E) 64
5y - 3x = 75 and so y = 3x/5 + 15   When x = 0, then y = 15.   When y = 0, then x = -25   The slope is 3/5, so the slope of line S is -5/3.   Through the point (-25, 0), 0 = -5(-25)/3 + c   The y-intercept is c = -125/3 &lt; -41.   Thus the perpendicular line S can have y-intercepts from -41 up to 14.   The number of possible lines is   41 + 14 + 1= 
<gadget id="calculator">  41 + 14 + 1</gadget>
<output>56</output>
56   The answer is 56.
<result>C</result>
Line Q has the equation 5y – 3x = 75. 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.)