Question

Which of the following gives an example of a function that is not linear
9x + 3y - 18 = 0
y = 1/6 x + 2/3
y = x^2 - 3x + 2.25
2x + 3y =16

Answer 1

To determine which of the given equations represents a function that is not linear, we can analyze each equation:

1. **9x + 3y - 18 = 0**:
- This can be rewritten as \(3y = -9x + 18\) or \(y = -3x + 6\). This is a linear function.

2. **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.

3. **y = x^2 - 3x + 2.25**:
- This is a quadratic equation (the highest exponent of x is 2). Quadratic functions are not linear.

4. **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**.