Question

Which equation represents a nonlinear function?

x(y – 5) = 2

y – 2(x + 9) = 0

3y + 6(2 – x) = 5

2(y + x) = 0

Answer 1

The correct answer is: A: x(y – 5) = 2

Explanation:

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Answer 2

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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