Understanding Linear Functions | Definition, Graphing, and Applications

Linear Function

A linear function is a mathematical function that can be expressed in the form f(x) = mx + b, where m and b are constants

A linear function is a mathematical function that can be expressed in the form f(x) = mx + b, where m and b are constants.
– The variable x is the independent variable, and represents the input or the value to be substituted into the function.
– The constant m corresponds to the slope of the line formed by the function.
– The constant b represents the y-intercept, which is the point where the line intersects the y-axis.

The graph of a linear function is always a straight line. The slope (m) determines the steepness and direction of the line. A positive slope means the line goes uphill from left to right, while a negative slope means the line goes downhill. A slope of zero means the line is horizontal.

The y-intercept (b) represents the value of the function when x is zero. In other words, it is the point where the line crosses the y-axis.

Linear functions are useful in many areas of mathematics and real-life applications. They can model relationships between variables that have a constant rate of change. For example, if you are driving at a constant speed, your distance traveled can be described by a linear function.

To graph a linear function, you can plot two points to determine the line. The y-intercept gives you one point, and then you can use the slope to find a second point. From there, you can connect the dots to draw the line.

Linear functions are fundamental in algebra and calculus, and they serve as building blocks for more complex functions. They are used in systems of equations, optimization problems, and various other mathematical concepts.

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