## Choosing Variables For a Straight Line

Not every equation naturally gives rise to a straight line. If we have variables and related by or and related by then graphs of against or against will not result in a straight line. We are however not restricted to plot against or against We can often rearrange an equation into a form which will give a straight line if we plot a suitable function of one variable against a suitable function of the other. In order to do this we need to:

• Identify which symbols in the equation are variables and which are constants.

• The symbols that correspond to and must be variables and the symbols that correspond to and must be constants.

• If a variable is cubed, square rooted or the reciprocal, log or exponential is taken, the result is still a variable and may still be used to label one of the axes.

• Any function of the readings may be used to label the axes, since the result is still a variable.

• Sometimes the physical quantities use the same symbols as in our notation e.g. is used to denote the speed of light. Do not get these confused.

For the equation above, taking natural logs results in a straight line. For the equation above, plotting against results in a straight line with gradient -1 and intercept since  