Determine whether the table of values below represents a linear function. If it represents a linear function, write the function. If it does not represent a linear function, explain why not.

Answer:

The equation of a linear function is:

Step-by-step explanation:

Given the table

x                    y

-10               -16

-3                 -2

1                    6

2                   8

Determining the slope between the points (-10, -16), (-3, -2)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-10,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-2\right)[/tex]

[tex]m=\frac{-2-\left(-16\right)}{-3-\left(-10\right)}[/tex]

[tex]m=2[/tex]

Determining the slope between the points (-3, -2), (1, 6)

[tex]m=\frac{6-\left(-2\right)}{1-\left(-3\right)}[/tex]

[tex]m=2[/tex]

Determining the slope between the points (1, 6),(2, 8)

[tex]m=\frac{8-6}{2-1}[/tex]

[tex]m = 2[/tex]

As the slope between the points is the same. Thus, the table represents the linear function.

Using the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

substituting the values m = 2 and any point let say (1, 6)

[tex]y - 6 = 2(x-1)[/tex]

[tex]y-6 = 2x-2[/tex]

[tex]y = 2x-2+6[/tex]

[tex]y = 2x+4[/tex]

Therefore, the equation of a linear function is:

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