Linear relations > Linear models
1234Linear models

Theory

Take a look at this applet.

Sometimes a relationship between two variables y and x is given in the form of a table of observations (measurements). If these points seem to lie (roughly) on a straight line, then you can set up a corresponding linear model. This comes with a linear function of the form y = a x + b .

If the line passes through ( 10 , 210 ) and ( 30 , 300 ) , then you can determine the linear formula as follows:

  • x increases with 30 - 10 = 20 ;

  • y increases with 300 - 210 = 90 ;

  • if therefore x increases with 1 , then y increases with 90 20 = 4.5 ;

  • the gradient of the line is therefore 4.5 ;

  • the required formula is then y = 4.5 x + b ;

  • ( 10 , 210 ) has to lie on the line, therefore 210 = 4.5 10 + b , so b = 165 .

The formula of the line is: y = 4.5 x + 165 .

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