Mastering Mathematics Smartly
by Wee Wen Shih

If a scatter diagram shows a non-linear relationship between variables, one has to carry out transformation to make the relationship linear to sketch a straight line. One may think that this is new and may not understand.

Interestingly, knowledge of Additional Mathematics from O-level is extremely helpful. Recall the following facts you have learnt previously in secondary mathematics:

• y = ax^b can be transformed to: ln y = ln a + b ln x. So, we will plot ln y against ln x.
  
  
• y = ab^x can be transformed to: ln y = ln a + x(ln b). So, we will plot ln y against x.
  
  
• For the relationship y = ax^2 + b, we will plot y against x^2.
  
  
• For the relationship y = a/x + b, we will plot y against 1/x.
  
  
• y = (ax) / (x + b) can be transformed to: 1/y = 1/a + (b/a)(1/x). So, we will plot 1/y against 1/x.

In each case, we are rewriting the non-linear function in the form of Y = mX + c, which is a linear expression. The rest of the steps to find gradient and y-intercept in the transformed expression is routine with the aid of GC.