Question

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

x −2 −1 0 1 2
y −4 −2 0 2 −2

A - The table represents a nonlinear function because there is not a constant rate of change in the output values.
B - The table represents a nonlinear function because there is not a constant rate of change in the input and output values.
C - The table represents a linear function because there is a constant rate of change in the input and output values.
D - The table represents a linear function because there is not a constant rate of change in the input and output values.

Answer 1

The correct option is,

The table represents a linear function because there is not a constant rate of change in the input and output values.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table is shown in figure.

Now,

For Table;

The equation of line is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - (-4) = (-2 - (-4)) / (- 1 - (-2))  (x - (-2))

⇒ y + 4 = 2/1 (x + 2)

⇒ y + 4 = 2 (x + 2)

⇒ y + 4 = 2x + 4

⇒ y = 2x

Thus, The table represents a linear function because there is not a constant rate of change in the input and output values.

Learn more about the equation of line visit:

https://brainly.com/question/18831322

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