A function expressed in the form f(x) = mx + b is known as a linear function. In this equation:
- f(x) represents the output of the function,
- x is the input variable,
- m is the slope of the line, which indicates how steep the line is, and
- b is the y-intercept, which is the point at which the line crosses the y-axis.
The slope m determines the rate of change of the function; for instance, if m is positive, the function increases as x increases, whereas if m is negative, the function decreases as x increases. The y-intercept b tells us the value of f(x) when x=0.
Linear functions are vital in various fields such as mathematics, physics, and economics, as they describe relationships that change at a constant rate. The graph of a linear function is always a straight line, making them easy to analyze and interpret.
In summary, the function f(x) = mx + b is a straightforward yet powerful concept in mathematics that helps us understand linear relationships between variables.