Understanding Linear Functions | Definition, Equation, and Graphing

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 is one of the simplest and most commonly used types of functions in mathematics. The general form of a linear function is:

f(x) = mx + b

where:
– f(x) represents the dependent variable, or the output of the function.
– x represents the independent variable, or the input to the function.
– m is the slope of the line, which determines the rate of change of the function.
– b is the y-intercept, which represents the value of f(x) when x = 0.

The slope, m, governs the steepness of the line. A positive slope means that as x increases, f(x) also increases. A negative slope means that as x increases, f(x) decreases.

The y-intercept, b, is the value of f(x) when x = 0. It represents the point where the line crosses the y-axis.

Using the equation of a linear function, you can determine the value of f(x) for any given x, or you can find the x-intercept or y-intercept of the line. You can also determine the slope by comparing the change in f(x) to the corresponding change in x.

For example, let’s consider the linear function f(x) = 2x + 3. In this case, the slope is 2, meaning that as x increases by 1, f(x) increases by 2. The y-intercept is 3, indicating that the line crosses the y-axis at the point (0, 3).

By plotting points on a graph and connecting them with a straight line, you can visualize the linear function and understand its behavior.

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