Linear and Non-Linear Relations

 
6.1

  Linear and Non-Linear Relations

A linear relation is a relationship between two variables that when plotted on a graph gives a straight line.
 
A line of best fit is a straight line that best expresses the relationship between a set of data points
  Lines of best fit have the following characteristics: 
 
  1. It passes through as many points as possible..
  2. Points are evenly distributed on both the left and right sides of the line.

     

 

Example
 
 

The diagram shows the line of best fit by plotting \(\dfrac{y}{x}\) against \(x\).

Find the relation between \(y\) and \(x\).

 
 
 
 

Note that the gradient is \(m=\dfrac{5-1}{6+2}=\dfrac{1}{2}\) which passing through \((6,5)\).

\(\begin{aligned} \dfrac{y}{x}&=mx+c\\ 5&=\dfrac{1}{2}(6)+c\\ 5&=3+c\\ c&=2. \end{aligned}\)

Therefore, the equation is \(\dfrac{y}{x}=\dfrac{1}{2}x+2\) or \(y= \dfrac{1}{2}x^2+2x\).