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Linear

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Saved by PBworks
on August 13, 2007 at 11:08:16 pm
 

Linear Function

 

Definition:

A linear function is a polynomial of degree one.  The graph of a linear function is a straight line.

 

Formula:

General Form: Ax + By + C = 0

 

Slope-Intercept Form: y = mx + b

 

Point-Slope Form: (y - y1) = m(x - x1)

 

Two-Point Form:  (y - y1) = [(y2 - y1)/(x2 - x1)](x - x1)

 

Real-World Example: 

So I was watching CSI last night and when Grisom got to the crime scene, he had the guy from the morgue take a reading of the recently deceased liver temperature.  He then said that a person's liver temperature falls at a rate of 1.5 degrees per hour after death.  This would give a linear functin.  I was thinking that Newton's Law of Cooling, or some other exponential decay function, might give a better estimation of time of death.  After a little bit of internet research, I found a bunch of television crime dramas all use the 1.5 degree/hr rule.  The accuracy of this thumb rule is questionable.  The rate of temperature deline (Algor Mortis) can be effected by body size, clothing, air temperature and humidity.  The University of Dundee School of Forensic Medicine has some interesting notes about using temperature to determine the time of death.

 

Linear Function Photo:

 

 

 

This is a picture of the Chapel Bridge in Lucern, Switzerland that I took while on vacation.  The roof of this footbridge, originally constructed in 1333, can be modeled by a linear function.  I set the origin at the base of the stone tower.  Given this somewhat arbitrary origin, the roof of the bridge could be modeled by the functio y = 0.25x + 2.

 

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