## linear function

### A linear function is a type of mathematical function that exhibits a linear relationship between its input and output

A linear function is a type of mathematical function that exhibits a linear relationship between its input and output. It is expressed in the form of f(x) = mx + b, where m represents the slope of the function and b represents the y-intercept.

In a linear function, the rate of change between the input (x) and output (f(x)) is constant. This means that as x increases or decreases by a certain amount, the output also increases or decreases by a corresponding multiple of that amount.

The slope (m) of a linear function determines the steepness of the graph. If the slope is positive, the graph will have an upward or positive direction. If the slope is negative, the graph will have a downward or negative direction. A slope of zero indicates that the function is a horizontal line.

The y-intercept (b) is the point where the graph intersects the y-axis. It represents the value of the dependent variable (f(x)) when the independent variable (x) is equal to zero.

Linear functions are commonly used to model relationships between two variables in various fields, such as economics, physics, and engineering. They provide a simple way to represent and analyze straight-line relationships. The graph of a linear function is a straight line on a coordinate plane.

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