A function is considered linear if it can be written in the form \( y = mx + b \), where \( m \) and \( b \) are constants. Linear equations can also be expressed in standard form \( Ax + By = C \).
Among the given options:
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\( 9x + 3y - 18 = 0 \): This can be rearranged to \( y = -3x + 6 \). This is a linear function.
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\( y = x^2 - 3x + 2.25 \): This is a quadratic function because of the \( x^2 \) term. This is not a linear function.
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\( 2x + 3y = 16 \): This can be rearranged to \( y = -\frac{2}{3}x + \frac{16}{3} \). This is a linear function.
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\( y = \frac{1}{6}x + \frac{2}{3} \): This is clearly in the form \( y = mx + b \), and hence it is a linear function.
Therefore, the example of a function that is not linear is:
\( y = x^2 - 3x + 2.25 \).