Understanding Linear Functions | Definition, Graphing, and Applications

Linear Function (Equation)

A linear function is a mathematical function that can be represented by a straight line when graphed on a coordinate plane

A linear function is a mathematical function that can be represented by a straight line when graphed on a coordinate plane. It has the form of y = mx + b, where m is the slope or rate of change of the line, and b is the y-intercept, which is the value of y when x is equal to zero.

The slope, represented by m, determines how steep the line is. If the slope is positive, the line will be increasing from left to right, while a negative slope will result in a decreasing line. A zero slope indicates a horizontal line, and an undefined slope means a vertical line.

The y-intercept, represented by b, is the point where the line intersects the y-axis. The y-coordinate of this point gives the initial value of the dependent variable (y) when x is equal to zero.

To graph a linear function, you can plot the y-intercept first, and then use the slope to find additional points on the line. You can find the slope by determining the change in y (vertical change) divided by the change in x (horizontal change) between any two points on the line.

Linear functions are commonly used to represent many real-life scenarios, such as distance-time relationships, cost-profit analysis, and temperature conversions. They are also fundamental in algebra and are widely studied in mathematics.

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