Which of the following gives an example of a function that is not linear?(1 point)

Question

Responses

2x+3y=16
2 x plus 3 y equals 16

9x+3y−18=0
9 x plus 3 y minus 18 equals 0

y=x2−3x+2.25
y equals x squared minus 3 x plus 2.25

y=1/6x+2/3

Answer 1

A function is considered non-linear if it cannot be represented in the form \(y = mx + b\) (where \(m\) and \(b\) are constants).

Let's evaluate the equations provided:

1. \(2x + 3y = 16\): This is a linear equation. It can be rearranged into the slope-intercept form \(y = -\frac{2}{3}x + \frac{16}{3}\).

2. \(9x + 3y - 18 = 0\): This is also a linear equation. It can be rearranged into the form \(y = -3x + 6\).

3. \(y = x^2 - 3x + 2.25\): This is a quadratic function due to the \(x^2\) term, making it non-linear.

4. \(y = \frac{1}{6}x + \frac{2}{3}\): This is a linear equation in slope-intercept form.

Thus, the example of a function that is not linear is:

\(y = x^2 - 3x + 2.25\).