We see for each row the x coordinates are in arithmetic progression, with a constant difference between successive points. For example in A x coordinates 3-5=1-3. So for this to be a line, the same has to be true of the y coordinates; they have to be in arithmetic progression.
A. 5/2, 3/2, 1/2 is just 5,3,1 (constant factors don't matter) so those are in arithmetic progression like the x coordinates so we have a line.
B. 1/2, 1, 3/2. In AP, a line
C. -1/2, -1/3, -1/4 multiplying by common denominator -12 makes 6, 4, 3. Those aren't in arithmetic progression. Not a line.
D. 2,3,4 in AP, a line.
E. 3/4, 1 3/4, 2 3/4 mixed numbers but obvious AP.
Answer: C
