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

1 answer

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.