Variables and constants

A variable is a quantity to which an unlimited number of values can be assigned. Variables are denoted by the later letters of the alphabet. Thus, in the equation of a straight line,

$$\frac{x}{a} + \frac{y}{b} = 1$$

$x$ and $y$ may be considered as the variable coordinates of a point moving along the line. A quantity whose value remains unchanged is called a constant.

Numerical or absolute constants retain the same values in all problems, as $2$, $5$, $\sqrt{7}$, $\pi$, etc.

Arbitrary constants, or parameters, are constants to which any one of an unlimited set of numerical values may be assigned, and they are supposed to have these assigned values throughout the investigation. They are usually denoted by the earlier letters of the alphabet. Thus, for every pair of values arbitrarily assigned to $a$ and $b$, the equation

$$\frac{x}{a} + \frac{y}{b} = 1$$

represents some particular straight line.