Getting a Straight Line Graph

A straight line takes the form  
\[y=mx+c\]
. You may think that if two quantities are not linearly related it is impossible to get a straight line graph between them. THIS IS NOT TRUE! It is often possible to transform variables and plot transformed variables to get a straight line graph.
Example: The thin lens equation is  
\[\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\]
.
We can rewrite this as  
\[\frac{1}{v}=- \frac{1}{u}+\frac{1}{f}\]
. and plot  
\[\frac{1}{u}\]
  on the  
\[x\]
  axis against  
\[\frac{1}{v}\]
  on the  
\[y\]
  axis. The  
\[y\]
  intercept will be  
\[\frac{1}{f}\]
  and the gradient will be -1.
Example: The equation of radioactive decay is  
\[N=N_) \times e^{-\lambda t}\]
. We can transform this by taking logs, obtaining  
\[ln(N)=-\lambda t + ln(N_0) \]
. Now we can get a straight line by plotting  
\[ln(N)\]
  on the  
\[y\]
  axis against  
\[t\]
  on the  
\[x\]
  axis. The gradient will be  
\[- \lambda\]
  and the  
\[y\]
  intercept will be  
\[ln(N_0)\]
.
Example: Boyles Law for an ideal gas is given by  
\[pV=CONSTANT\]
  where  
\[p, : V\]
  are the pressure and volume respectively of an ideal gas. We can write this equation as  
\[p=\frac{CONSTANT}{V}\]
  and plot  
\[p\]
  on the  
\[y\]
  axis against  
\[\frac{1}{V}\]
  on the  
\[x\]
  axis. The  
\[y\]
  intercept will be 0 (the line will pass through the origin) and the gradient will be  
\[CONSTANT\]
.