Final answer:
The average rate of change of a function is represented by the slope in a linear equation, where the slope describes how the dependent variable changes for each unit increase in the independent variable. A slope of 4.83, for example, means a 4.83-point increase in one variable for each 1-point increase in another.
Step-by-step explanation:
The average rate of change of a function is typically associated with the slope in the context of linear equations. In slope-intercept form, the slope is represented by the coefficient of the x-term in the equation y = mx + b, where m is the slope and b is the y-intercept. For instance, if we consider a line graph where the horizontal axis represents the time and the vertical axis represents some dependant variable, a y-intercept of 9 and a slope of 3 means that there is a vertical rise of 3 units for every 1-unit horizontal increase along the axis. This indicates a steady rate of change since the slope is constant along a straight line.
An example that illustrates the practical interpretation of slope is if we have an equation representing the relationship between scores on two different exams. If the slope of the line is 4.83, it signifies that for every additional point scored on the third exam, the final exam score increases by 4.83 points on average. This shows that the slope provides a measure of how one variable affects another in the linear relationship between them.
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