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Linear and Non-Linear Relations

6.1 Linear and Non-Linear Relations
 
The image contains two main sections. On the left, there is a text that says ‘Distinguish Between Linear and Non-Linear Relationships’ with the Pandai logo below it. On the right, there is a text on a notecard that reads, ‘A graph that forms a straight line is a linear relationship while a graph that does not form a straight line is a non-linear relationship.’ An arrow points from the left text to the right notecard.
 
Definition
  • 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.
 
Line of Best Fit
Characteristic
  • It passes through as many points as possible.
  • Points are evenly distributed on both the left and right sides of the line.
Graph

A linear graph showing a line with a point on it.
 
Example
Question

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

Linear graph with two points intersecting on the line.

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

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 \(y= \dfrac{1}{2}x^2+2x\).
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.

Linear and Non-Linear Relations

6.1 Linear and Non-Linear Relations
 
The image contains two main sections. On the left, there is a text that says ‘Distinguish Between Linear and Non-Linear Relationships’ with the Pandai logo below it. On the right, there is a text on a notecard that reads, ‘A graph that forms a straight line is a linear relationship while a graph that does not form a straight line is a non-linear relationship.’ An arrow points from the left text to the right notecard.
 
Definition
  • 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.
 
Line of Best Fit
Characteristic
  • It passes through as many points as possible.
  • Points are evenly distributed on both the left and right sides of the line.
Graph

A linear graph showing a line with a point on it.
 
Example
Question

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

Linear graph with two points intersecting on the line.

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

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 \(y= \dfrac{1}{2}x^2+2x\).
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.
Chapter : Linear Law
Topic : Linear and Non-Linear Relations
Form 4 Additional Mathematics
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