A function is considered linear if it can be expressed in the form \(y = mx + b\), where \(m\) and \(b\) are constants, or if it can be rearranged to this form. Let's evaluate each of the provided equations:
- \(2x + 3y = 16\) - This can be rearranged to \(y = -\frac{2}{3}x + \frac{16}{3}\), which is linear.
- \(y = x^2 - 3x + 2.25\) - This is a quadratic equation due to the \(x^2\) term, making it nonlinear.
- \(9x + 3y - 18 = 0\) - This can be rearranged to \(y = -3x + 6\), which is linear.
- \(y = \frac{1}{6}x + \frac{2}{3}\) - This is already in the form \(y = mx + b\), making it linear.
From these evaluations, the only example of a function that is not linear is:
\(y = x^2 - 3x + 2.25\).