Understanding Linear Functions: Definition, Graphing, and Applications

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 considered to be the simplest type of function and is often used to model relationships between two variables.

The general form of a linear function is given by:

f(x) = mx + b

Where:
– “f(x)” represents the output or dependent variable.
– “x” represents the input or independent variable.
– “m” represents the slope of the line.
– “b” represents the y-intercept, which is the value of the dependent variable when the independent variable is 0.

The slope (m) determines the steepness or incline of the line. If the slope is positive, the line increases as the input variable increases. If the slope is negative, the line decreases as the input variable increases. A slope of 0 would result in a horizontal line.

The y-intercept (b) represents the point where the line crosses the y-axis. It gives the initial value of the dependent variable when the independent variable is 0.

To graph a linear function, you can plot two points on the coordinate plane, connect them with a straight line, and extend the line in both directions.

If you have two points (x1, y1) and (x2, y2), you can calculate the slope (m) using the formula:

m = (y2 – y1) / (x2 – x1)

Then, you can substitute one of the points and the calculated slope into the general form of a linear function to find the value of the y-intercept (b). Finally, you can graph the function using the slope and y-intercept.

It’s important to note that linear functions have a constant rate of change, meaning the change in the dependent variable is constant for every unit change in the independent variable.

Linear functions are commonly used in various fields such as physics, engineering, economics, and statistics to model and analyze relationships between variables.

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