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

Responses

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

y=x^2−3x+2.25
y equals x squared minus 3 x plus 2.25

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

y=1/6x+2/3

1 answer

A function is considered linear if it can be written in the form \( y = mx + b \), where \( m \) and \( b \) are constants. Linear equations can also be expressed in standard form \( Ax + By = C \).

Among the given options:

  1. \( 9x + 3y - 18 = 0 \): This can be rearranged to \( y = -3x + 6 \). This is a linear function.

  2. \( y = x^2 - 3x + 2.25 \): This is a quadratic function because of the \( x^2 \) term. This is not a linear function.

  3. \( 2x + 3y = 16 \): This can be rearranged to \( y = -\frac{2}{3}x + \frac{16}{3} \). This is a linear function.

  4. \( y = \frac{1}{6}x + \frac{2}{3} \): This is clearly in the form \( y = mx + b \), and hence it is a linear function.

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

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