To determine which of the given equations represents a function that is not linear, we can analyze each equation:
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9x + 3y - 18 = 0:
- This can be rewritten as \(3y = -9x + 18\) or \(y = -3x + 6\). This is a linear function.
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y = 1/6 x + 2/3:
- This is in the slope-intercept form \(y = mx + b\) where \(m = 1/6\) and \(b = 2/3\). This is also a linear function.
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y = x^2 - 3x + 2.25:
- This is a quadratic equation (the highest exponent of x is 2). Quadratic functions are not linear.
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2x + 3y = 16:
- This can be rewritten as \(3y = -2x + 16\) or \(y = -\frac{2}{3}x + \frac{16}{3}\). This is a linear function.
The function that is not linear is:
y = x^2 - 3x + 2.25.