If a linear function can be used to represent the data, the following must be true of the data set:
**The set must have a constant additive rate of change.**
A linear relationship between an independent variable \( x \) and a dependent variable \( y \) is represented by the equation \( y = mx + b \), where \( m \) is the slope (the constant additive rate of change) and \( b \) is the y-intercept. This means that for every unit increase in \( x \), \( y \) increases by a constant amount \( m \).
The other options are not necessarily true for a linear function:
- A constant multiplicative rate of change usually describes an exponential relationship, not a linear one.
- The values in the set do not need to be positive; they can be negative or zero.
- The values in the set do not necessarily need to be increasing; they can be decreasing or constant as long as the rate of change is constant.
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.
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