An introduction to mathematics, by A. N. Whitehead.

VARIABLES 21
(in any scale) of length along OX, any number y by y units (in any scale) of length along
OY. Thus if OM, along OX, be x units in
length, and ON, along OY, be y units in
length, by completing the parallelogram
OMPN we find a point P which corresponds
to the pair of numbers x and y. To each
point there corresponds one pair of numbers,
and to each pair of numbers there corresponds one point. The pair of numbers are
called the coordinates of the point. Then
the points whose coordinates satisfy some
fixed relation can be indicated in a convenient way, by drawing a line, if they all lie
on a line, or by shading an area if they are
all points in the area. If the relation can
be represented by an equation such as
x+y=l, or y2=x, then the points lie on a
line, which is straight in the former case and
curved in the latter. For example, considering only positive numbers, the points whose
coordinates satisfy x +y = 1 lie on the straight
line AB in Fig. 1, where OA = 1 and OB = 1.
Thus this segment of the straight line AB
gives a pictorial representation of the properties of the relation under the restriction to
positive numbers.
Another example of a relation between two
variables is afforded by considering the variations in the pressure and volume of a given
mass of some gaseous substance-such as air