# Ch1ppt - LinearFunctions Chapter1 LinearFunctions n 1....

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Linear Functions Chapter 1

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Linear Functions n 1.2   Linear Functions and Applications
Equations of Lines Equation Description ax  +   by = c Standard form  0,  b  „  0,  x -intercept =  c/a,     y -intercept =  c/b m  =  –a/b. y = mx + b Slope-intercept form : slope  m , y-intercept  b y – y 1  = m ( x – x 1) Point-slope form : slope  m , line passes through  ( x 1, y 1)

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Slopes of Lines m  = 0 (Horizontal  line) Undefined slope (Vertical line)
1.2   Applications of Linear  Functions n Many situations involve two variables,  x   (independent variable) and  (dependent variable),  with a linear relationship. n If  y  is expressed in terms of  x , then  y  is a  linear  function  of  x . n For any value of  x , the corresponding value of  y   can be calculated.

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Linear Functions n Examples n y  = 3 x  + 7 n 12 x  + 6 y  = 24 fi   = -2 x   + 4 n f (x)  Notation:  Letters can be used to name  functions. n if  f  is used to name  y  = 3 x  + 7 n f ( x ) = 3 x  + 7 n f (2) = 3(2) + 7 = 13 n f (-2) = 1,  f (0) = 7,  f (1) = 10...
Linear Functions n A relationship  f  defined by y = f(x) = mx + b, n for real numbers  m  and  b , is a  linear  function

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Applications of Linear Functions n Basic business relationships: n Revenue = Price ∙  Quantity n Total Cost = Fixed Costs + Variable Costs n Average Cost = Total Cost  ÷  Quantity n Profit = Revenue – Total Costs
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