Graphs show relationships between the depicted variables. If this relationship follows a certain rule, or law, then the graph of that relationship will show a certain pattern, which can be described by a formula. The x-axis is sometimes described as the abscissa, and the y-axis as the ordinate.

The linear relationship

y = k.x is the simplest example of a linear relationship. When plotting this on a graph, we could calculate y for several x's, plot each as a point and then join them by a line. We know that this line will be a straight line passing through zero, with a slope α proportionate to k (see Figure 22). If we wished to obtain the sum of all y's for their respective x's up to X, this would be given as the area of triangle XYO, otherwise known as the area under the line k, and the process of obtaining this area is called integration. More on integrals in the chapter on flow measurement.

Rectangular hyperbola

An inverse, or reciprocal relationship, y = k/x, is depicted by a rectangular hyperbola, k being a constant. y = 1/x is a specific form of this relationship when k = 1. The line representing this function is symmetrical across an axis passing through zero at 45°. It asymptotically approaches (never quite reaches) both axes, i.e. neither x nor y can be zero.