Line Q has the equation 5y – 3x = 90. 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.)	Select:
A) 58 B) 61 C) 64 D) 67 E) 70
5y - 3x = 90 and so y = 3x/5 + 18   When x = 0, then y = 18.   When y = 0, then x = -30   The slope is 3/5, so the slope of line S is -5/3.   Through the point (-30, 0), 0 = -5(-30)/3 + c   The y-intercept is c = -50.   Thus the perpendicular line S can have y-intercepts from -49 up to 17.   The number of possible lines is   49 + 17 + 1= 
<gadget id="calculator">  49 + 17 + 1</gadget>
<output>67</output>
67   The answer is 67.
<result>D</result>
Line Q has the equation 5y – 3x = 90. 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.)