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Which statement best explains whether the following graph represents a linear or nonlinear function?

coordinate plane with a graph that passes through the points negative 4 comma 0 and negative 2 comma negative 1 and 0 comma negative 2

The graph represents a linear function because there is a constant rate of change.
The graph represents a linear function because the rate of change is not constant.
The graph represents a nonlinear function because there is a constant rate of change.
The graph represents a nonlinear function because the rate of change is not constant.

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anbu40

Answer:

The graph represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Linear or nonlinear function:

  • Find the rate of change.
  • If the rate of change is constant, then the given graph represents the linear function.
  • If the rate of change is not a constant, then the given graph represents a nonlinear function.

(-4,0); (-2, -1); (0, -2)

Take any two points and find the rate of change.

(-4, 0) & (-2, -1)

[tex]\sf rate \ of \ change = \dfrac{difference \ in \ y}{difference \ in \ x}[/tex]

                     [tex]\sf =\dfrac{-1-0}{-2-(-4)}=\dfrac{-1}{-2+4}\\\\\\=\dfrac{-1}{2}\\\\\\=\dfrac{-1}{2}[/tex]

(-2, -1) & (0, -2)

[tex]\sf Rate \ of \ change = \dfrac{-2-(-1)}{0-(-2)}\\\\\\~~~~~~~~~~~~~~~~~~~~ = \dfrac{-2+1}{2}\\\\\\~~~~~~~~~~~~~~~~~~~~ = \dfrac{-1}{2}[/tex]

(-4,0) & (0 , -2)

[tex]\sf Rate \ of \ change = \dfrac{-2-0}{0-(-4)}\\\\\\~~~~~~~~~~~~~~~~~~~~ = \dfrac{-2}{0+4}=\dfrac{-2}{4}\\\\\\~~~~~~~~~~~~~~~~~~~~ = \dfrac{-1}{2}[/tex]

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

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