The minus 16 at the end is directly the reason why. Think of y = 1/x, and subtracting 16 from both sides to get y-16 = (1/x) - 16. The y-16 will shift every point down 16 units. For instance, the point (1, 1) moves to (1, -15).
An infinite number of solutions means a coincident line...it is the same line 3y = 2x - 9...divide by 3 y = 2/3x - 3...hmm...same line as answer choice b....they are coincident lines and have infinite solutions