Linear Function

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Linear function

A function [math]f\,[/math] defined for all real [math]x\,[/math] by a formula of the form


  • It's called a linear function because its graph is a straight line.
  • The number [math]b\,[/math] is called the y-intercept of the line; it is the y-coordinate [math](0,b)\,[/math] where the line cuts the y-axis.
  • The number [math]a\,[/math] is called the slope of the line.


[math]\text{Linear function }\,[/math][math]f(x)=3x-5\,[/math]
[math]n\,[/math] [math]f(n)\,[/math]
[math]-5\,[/math] [math]-20\,[/math]
[math]-4\,[/math] [math]-17\,[/math]
[math]-3\,[/math] [math]-14\,[/math]
[math]-2\,[/math] [math]-11\,[/math]
[math]-1\,[/math] [math]-8\,[/math]
[math]0\,[/math] [math]-5\,[/math]
[math]1\,[/math] [math]-2\,[/math]
[math]2\,[/math] [math]1\,[/math]
[math]3\,[/math] [math]4\,[/math]
[math]4\,[/math] [math]7\,[/math]
[math]5\,[/math] [math]10\,[/math]