Question

Which table of values represents a linear function?

Answer 1

`D`

Explanation:

.

A linear function has a constant slope. This means that for any equal change in `x` there is an equal change in `y`.

In `D`,

`x_1=-2, x_2=-1, x_3=0, and x_4=1`

`y_1=0, y_2=2, y_3=4, and y_4=6`

`slope=m=(y_2-y_1)/(x_2-x_1)=(2-0)/(-1-(-2))=2/(-1+2)=2/1=2`

`m=(y_3-y_2)/(x_3-x_2)=(4-2)/(0-(-1))=2/1=2`

`m=(y_4-y_3)/(x_4-x_3)=(6-4)/(1-0)=2/1=2`

As you can see, the slope is constant. Therefore, this is a linear function.