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Which statement best explains whether the data in the following table represents a linear or nonlinear function?


x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.

Respuesta :

anbu40

Answer:

The table represents a linear function because the graph shows a constant rate of change.

Step-by-step explanation:

To determine whether the data represents a linear or non-linear function:

 In the linear function, the rate of change of y with respect to x remains the same/constant. The rate of change is called the slope.

 [tex]\boxed{\sf Slope =\dfrac{difference \ in \ y}{difference \ in \ x} =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Find the rate of change. If the rater of change is constant, then its is linear function.

  • (-4,4) & (-1 ,2.5)

         [tex]\sf \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2.5-4}{-1-(-4)}[/tex]

                      [tex]\sf = \dfrac{-1.5}{-1+4}=\dfrac{-1.5}{3}\\\\\\=\dfrac{-1.5*10}{3*10}=\dfrac{-15}{30}\\\\\\=\dfrac{-1}{2}[/tex]

  •      ((-1,2.5) & (0,2)

            [tex]\sf \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-2.5}{0-(-1)}\\\\\\~~~~~~~~~~=\dfrac{-0.5}{1}=\dfrac{-0.5*10}{1*10}\\\\\\~~~~~~~~~~=\dfrac{5}{10}\\\\\\~~~~~~~~~~=\dfrac{1}{2}\\[/tex]

  • (0,2) & (4, 0)

             [tex]\sf \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}\\\\\\~~~~~~~~~~~ =\dfrac{2}{4}\\\\~~~~~~~~~~~ = \dfrac{1}{2}[/tex]

As the rate of change is constant, the given data represents linear function.

           

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