California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

Which aspect is essential for the definition of a linear function?

1. The graph is a curve

2. It has a variable slope

3. The graph is a straight line

4. It has no y-intercept

The correct answer is: The graph is a straight line

The key characteristic of a linear function is that its graph forms a straight line when plotted on a coordinate system. This attribute signifies that the relationship between the variables is direct and consistent, meaning the change in one variable results in a proportional change in another. In algebra, a linear function is typically expressed in the form \(y = mx + b\), where \(m\) represents the constant slope and \(b\) is the y-intercept. The straight line representation indicates that regardless of the x-value, the rate of change in y remains constant, distinguishing linear functions from other types of functions that might involve curves or varying slopes. This understanding clarifies that a linear function does not have a variable slope, as the slope must be constant across all values of x. Additionally, while linear functions can have a y-intercept, claiming that they have "no y-intercept" is contrary to their definition, as they can intersect the y-axis at different points. Thus, recognizing the requirement for the graph to be a straight line is fundamental to understanding what constitutes a linear function.