Line Q has the equation 5y – 3x = 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.)	Choose the correct choice from the following: A) 22 B) 33 C) 36 D) 41 E) 58
5y - 3x = 30 and so y = 3x/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 &lt; -16.   Thus the perpendicular line S can have y-intercepts from -16 up to 5.   The number of possible lines is   16 + 5 + 1= 
<gadget id="calculator">  16 + 5 + 1</gadget>
<output>22</output>
22   The answer is 22.
<result>A</result>
Line Q has the equation 5y – 3x = 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.)