Question

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

Explanation:

To determine which statement is true for a data set representable by a linear function, recall the definition of a linear function. A linear function has the form \( y = mx + b \), where \( m \) (the slope) represents the rate of change. The rate of change for a linear function is constant and is an additive rate of change (since for each unit increase in \( x \), \( y \) changes by \( m \), which is an addition or subtraction).

• A constant multiplicative rate of change is characteristic of exponential functions, not linear functions.
• The values in the set do not need to be positive (e.g., a linear function can have negative values, like \( y = -2x + 3 \)).
• The values in the set do not have to be increasing; a linear function with a negative slope (e.g., \( y = -x + 5 \)) will have decreasing values as \( x \) increases.

So, the set must have a constant additive rate of change.

Answer:

The set must have a constant additive rate of change.