- In the x-y plane, point (p, q) is a lattice point if both p and q are integers. Circle C has a center at (2, 1) and a radius of 6. Some points, such as the center (2, 1), are inside the circle, but a point such as (4, 1) is on the circle but not in the circle. How many lattice points are in circle C?
- Line Q has the equation 5y 3x = 45. 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 Ss exist? (Note: Intersections on one of the axes do not count.)
- Line M has a y-intercept of 4, and its slope must be an integer-multiple of 1/7. Given that Line M passes below (4, 1) and above (5, 6), how many possible slopes could Line M have?
