Which of the following represent(s) a non-linear relation?

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Correct option is

B



Options A, B and D are equations of lines. We prove that the points in option B don't lie on a line. Consider the line passing through first two points. Its equation is 

2−12y−12=0−(−4)x−(−4)

⟹−10y−12=4x+4

⟹2y−24=−5x−20

⟹5x+2y=4.

If we put (4,−6) into this equation, 

LHS=5×4+2×(−6)=8=4=RHS. Which means that the point (4,−6) does not lie on the line joining the points (−4,12) and (0,2). Which is what we wanted to show.

C and D

In case of A:

-7/-2=-14/-4=-24.5/-7=-28/-8= 3.5

In case if B:

6/-2= 12/-4=21/-7= 24/-8 = -3

In case of C:

4/-2≠ 16/-4≠49/-7≠64/-8

In case of D:

1.4/-2≠2/-4≠2.6/-7≠2.8/-8

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