Rate of change is a fundamental concept that measures how one quantity changes in relation to another. It tells us how fast something is changing. The formula is simple: rate of change equals the change in the dependent variable divided by the change in the independent variable. Let's see this with an example using distance and time.
There are three main types of rate of change. A positive rate of change means that as the independent variable increases, the dependent variable also increases. A negative rate of change means that as the independent variable increases, the dependent variable decreases. A zero rate of change means the dependent variable stays constant as the independent variable changes.
To calculate the rate of change between two points, we use the formula: rate equals delta y over delta x, which is y two minus y one over x two minus x one. Let's work through an example. We have point A at coordinates two comma four and point B at coordinates six comma twelve. The change in x is four, and the change in y is eight. So the rate of change is eight divided by four, which equals two.
Rate of change appears everywhere in real life. Speed is the rate of change of distance over time, like sixty miles per hour. Temperature change shows how heat varies over time. Population growth measures how many people are added each year. Stock prices show how investment values change daily. Even the slope of a hill represents the rate of change of height over horizontal distance.
To summarize what we've learned about rate of change: It measures how one quantity changes relative to another using the formula rate equals change in y divided by change in x. A positive rate means increasing values, negative means decreasing, and zero means constant. Rate of change appears everywhere in real life from speed and temperature to population growth and stock prices. Understanding this concept is essential for analyzing relationships between variables in mathematics and science.