A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can be used to represent the data?

The set must have a constant additive rate of change.
The set must have a constant multiplicative rate of change.
The values in the set must be positive.
The values in the set must be increasing.

The set must have a constant additive rate of change.

Option A.

Explanation:

A function has an additive rate of change if there is a consistent distinction between any two successive information and yield esteems. From the primary table we can watch a consistent distinction of - 6 among the y-values and a steady contrast of 2 among the x-values.

A linear function has a consistent additive rate of change, while a nonlinear capacity doesn't. For a table of qualities to be direct, the needy variable must have a steady pace of progress as the autonomous variable increments by 1.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.