Which equation represents a nonlinear function?x(y – 5) = 2y – 2(x + 9) = 03y + 6(2 – x) = 52(y + x) = 0

The correct answer is:  [A]:  " x(y – 5) = 2 " .
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Consider:
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Choice:  [A]:  " x(y–5) = 2 " ; 

Divide each side by "x" ;

" [x(y – 5)] / x  = 2/x " ; 

  →  y – 5 = 2/x  ;

Add "5" to each side of the equation:

y – 5 + 5 = 2/x + 5 ;

  →  y = 2/x + 5  ;  not a line;  since one cannot divide by "zero" ; there would be no "point" on the graph at "x = 0".  So, this answer choice:  [A] is correct.
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Choice [B]:
 
y -2x -18 = 0 

y - 2x = 18

y = 18 + 2x ;  y = 2x + 18 ; is a line.
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Choice C)  3y + 12 - 6x = 5 ; 

3y = 5 - 12 + 6x ; 

3y = -7 + 6x ;  3y = 6x - 7 ;  y = 6x/3 - 7/3 ;  y = 2x - 7/3 ;  is a line.
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Choice:  [D]:

2(y+x) = 0 ;

[2*(y+x)] / 2 = 0/2 ;  y + x = 0 ;  y = -x ;  is a line.
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