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PRERNA FOR IAS
RATE OF CHANGE
1. Rate of Change
Rate of change describes how one quantity changes in relation to another quantity. It measures the amount of change in one variable compared to the change in another variable. This concept is widely used in mathematics, science, economics, and everyday situations such as speed, growth, and population studies.
2. Formula for Rate of Change
The rate of change is calculated using:
Rate of Change = (y₂ − y₁)/(x₂ − x₁)
This formula compares the change in y-values to the change in x-values. It helps determine how quickly one quantity changes relative to another and is fundamental in algebra and calculus.
3. Slope of a Line
The rate of change of a linear function is called its slope. The slope indicates how steep a line is and whether it rises or falls. A positive slope rises from left to right, while a negative slope falls from left to right.
4. Change in y
The quantity y₂ − y₁ represents the change in the y-values. It measur
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