Understanding Linear Functions | Definition, Graphing, and Real-World Applications

Linear Function

A linear function is a mathematical function that can be represented by a straight line on a graph

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept (the value of f(x) when x = 0). In other words, a linear function describes a relationship between two variables such that as one variable changes by a constant rate, the other variable changes by a proportional amount. The slope (m) determines how steep or flat the line is, while the y-intercept (b) represents the value of the function at the point where the line intersects the y-axis.

The key characteristic of a linear function is that it has a constant rate of change. This means that for every unit increase in the input variable (x), the output variable (f(x)) increases or decreases by the same amount determined by the slope. If the slope is positive, the function is increasing; if the slope is negative, the function is decreasing.

Linear functions are often used to model real-world scenarios where two variables are linearly related, such as distance versus time, cost versus quantity, or temperature versus time. They are fundamental in algebra and provide a basis for more complex mathematical concepts and applications.

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