Linear Functions
A linear function is a mathematical function that represents a straight line on a graph
A linear function is a mathematical function that represents a straight line on a graph. It is an algebraic function of the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept. The slope (m) represents the rate of change or the steepness of the line, while the y-intercept (b) is the value of y when x is zero.
The graph of a linear function is a straight line that extends infinitely in both directions. The slope of the line determines whether it is increasing, decreasing, or parallel to the x-axis. If the slope is positive, the line rises from left to right, while a negative slope causes the line to fall from left to right. If the slope is zero, the line is horizontal.
Linear functions are widely used in various fields, such as physics, economics, engineering, and business, to model relationships between variables that show a constant rate of change. They are relatively simple to work with algebraically and provide a foundation for understanding more complex functions.
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