# Graphs of Two Variable Functions

Many types of economic problems require that we consider two variables at the same time. A typical example is the relation between price of a commodity and the demand or supply of that commodity. The relation can be described algebraically by a two variable function or equation. But it is often useful to represent the relation in a two-dimensional graph. Such a graph is known as a scatter diagram. This is a useful device because if there is a simple relationship between the two variables, it is readily observable once the data are plotted. As the proverb says, “a picture is worth a thousand words.”

To represent a function graphically we use two perpendicular lines called axes. Their point of intersection is called the origin. This method of representation is called the Cartesian coordinate system or plane. The numerical value of one variable is measured along the bottom or horizontal axis. The horizontal axis is called the x axis. The numerical value of the other variable is measured along the side or vertical axis. The vertical axis is called the y axis. The four sections into which the graph is divided are called quadrants. Units of length are indicated along the two axes.

Note that there are four quadrants. If x is positive we move to the right. If x is negative we move to the left. If y is positive we move up. If y is negative we move down. ## Coordinates

Coordinates allow us to look at the relationship between pairs of numbers and points in the plane. Coordinates give the location of a point, P, in relation to the origin.

We have an x coordinate and a y coordinate.

Let (x, y) represent the point whose coordinates are the numbers x and y. Note that the x coordinate comes first. The two coordinates tell us how far we must go first along the x axis and then along the y axis until the point is reached.

Plotting coordinates: some examples

Example 1

Find the following points

point a (2, 4)
point b (4,-6)
point c (-2,-6)
point d (-6, 2) Example 2

p = the price per dollar of a crate of vegetables
f(p) = the supply in thousands of crates

A store manager has the following data which relate the price of a crate of vegetables to the supply:

 price 4 6 8 10 14 supply 2 14 23 27 29

What do the data tell us? The graph shows that as we might expect an increase in price is associated with an increase in supply. [Index]