Western Governors University (WGU) MATH1200 C957 Applied Algebra Practice Exam

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In terms of a linear function, what can be said about the rate of change?

It is always decreasing

It is constantly zero

It is always the same

In a linear function, the rate of change is represented by the slope of the line. The slope indicates how much the dependent variable (often \(y\)) changes for a unit change in the independent variable (often \(x\)). For linear functions, this slope remains constant throughout the entire function, meaning that for every increase in \(x\), there is a consistent and predictable increase (or decrease) in \(y\).

This constancy is a defining feature of linear functions, which differentiates them from other types of functions, such as quadratic or exponential functions, where the rate of change can vary. Thus, the rate of change being always the same is a hallmark quality of linear relationships and is why this choice is correct in describing the nature of a linear function.

It varies with each data point

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