Question

In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of a?

a = 2
a = 3
a = 19
a = 35


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.

Answer 1

I don't see the table in your message, so I can't pick which value of a is correct. Send the table (the x and y values) and I'll compute which choice gives a rate of change of −8.

How to find a: use the slope (rate of change) formula between two points (x1,y1) and (x2,y2):
(y2 − y1)/(x2 − x1) = −8
Plug in the coordinates (one of which will contain a) and solve that equation for a. If the x-values are consecutive integers, you can also just take successive differences in y; the missing y-value must differ from its neighbor by −8.

Second question answer: The set must have a constant additive rate of change.
Explanation: A linear function has a constant difference (additive change) in the dependent variable per unit change in the independent variable. A constant multiplicative rate of change indicates exponential data; values need not be positive or increasing for a linear model.