In the equation f(x) = ax + b, what does 'a' represent?

In the equation f(x) = ax + b, 'a' represents the slope of the line. The slope is a measure of how steep the line is and indicates the rate of change of the function with respect to the input variable x. Specifically, for every unit increase in x, the output f(x) changes by 'a' units.

This role of 'a' in defining the slope means that if 'a' is positive, the line rises as it moves from left to right, reflecting a positive relationship between x and f(x). Conversely, if 'a' is negative, the line falls, indicating a negative relationship. The value of 'a' directly affects how quickly the function increases or decreases, making it a crucial component in understanding linear functions.