Linear relations > Linear models
1234Linear models

Theory

Occasionaly the relation between y and x is given by a table with data. If the data (almost) fits a straight line, you can formulate a linear model. To describe the linear model you would use a linear formula such as y = a x + b .

Suppose the straight line goes through the points ( 10 , 210 ) and ( 30 , 300 ) , you would find the linear formula as follows:

  • x increases with 30 - 10 = 20;

  • y increases with 300 - 210 = 90;

  • if x were to increase with 1 , y would increase with 90 20 = 4 . 5 ;

  • the gradient of the line is, therefore 4.5 ;

  • the formula becomes y = 4.5 x + b ;

  • ( 10,210 ) is on the line, so 210 = 4.5 10 + b , which gives b = 165 .

The straight line corresponds to the formula: y = 4.5 x + 165 .

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