The average rate of change refers to the average rate at which a quantity changes over a given interval. It is calculated by finding the slope of the secant line between two points on a graph.
Think of driving from one city to another. The average rate of change would be your average speed over the entire journey, regardless of any fluctuations in speed along the way.
Instantaneous rate of change (IROC): The instantaneous rate of change represents the rate at which a quantity is changing at a specific point or instant. It is found by calculating the slope of the tangent line to that point on a graph.
Secant line: A secant line is a straight line that intersects two points on a curve. It can be used to calculate the average rate of change between those two points.
Slope: Slope measures how steep or flat a line is. It indicates how much y changes for every unit increase in x and can be used to find both average and instantaneous rates of change.
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