Saturday, August 9, 2008

Linear Functions

In elementary algebra and analytic geometry, the term linear function is sometimes used to mean a first degree polynomial function of one variable. These functions are called "linear" because they are precisely the functions whose graph in the Cartesian coordinate plane is a straight line.
Linear Functions is the most basic algebraic function. It is particularly useful in describing real-life situation. For instance, the Fahrenheit temperature scale is related to the Celsius temperature scale; the distance that a plane or a ship travels is related to the time it travels; the monthly salary of an employee is related to the number of hours the person has worked, etc. Each of these relationships can be described by a linear function.

Such a function can be written as: f(x) =mx+b where m and b are real constants and x is a real variable. The constant m is often called the slope or gradient, while b is the y-intercept, which gives the point of intersection between the graph of the function and the y-axis. Changing m makes the line steeper or shallower, while changing b moves the line up or down.

These functions are in slope-intercept form:

Examples: f(x)=3x+2 or y=3x+2
g(x)=4x+1

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