If (r,s) is on the line, then it must be the case that s = 3r+2
So, the question can be worded as "does s = 3r+2"

(1) If this equals zero, then either a) 3r+2-s = 0 or b) 4r+9-s = 0

a) --> s = 3r+2 (yes!)
b) --> s = 4r+9 (no!)
Insufficient

(2) Similar reasoning gives us:
c) --> s = 4r-6 (no!)
d) --> s = 3r+2 (yes!)
Insufficient

If statements (1) and (2) are true, then it must be the case that s = 3r+2, in which case (r,s) IS on the line.

Answer is C