AN INTRODUCTION TO GRAPHS
This is an introduction to drawing, reading, and understanding graphs. This material can also be
used as a review. Graphs are important because much of what is done in economics can be understood
more easily when translated into graphical form. You should think of a graph as a picture and try to see
what the picture shows.
THE ORIGIN, OVER AND UP
The explorer Fella della Hydrant was leading a tourist party through the North American
wilderness. At 10:06 a.m. on Saturday, July 18, 1784, he turned to his chief guide, a one-eyed
Frenchman named Quainto, and said "Where are we?"
Any useful reply given by Quainto requires
knowing where they started. The "Where are we?" question is really asking "Where are we compared to
some starting point?" The same is true for any location or point on a graph.
The starting point on a
graph, the point where measurement begins, is called the origin. Before we can know where we are on a
graph, or otherwise, we must know the origin.
Suppose that for Fella the origin point is Washington D.C. and Quainto replies,"We are 50.421
miles as the crow flies from Washington D.C." The problem is that 50.421 miles could be in any
direction. By itself, 50.421 miles would not locate Fella, Quainto, and party. What if Quainto replies,
“We are northwest of Washington D.C." The problem now is that Fella could be any distance northwest
of Washington D.C. What we are discovering is that location is not determined by one measure alone;
we need two measurements, both distance and direction, as well as an origin.
Consider a different example. Fella and Quainto are in a town called Pumpernickel. They make a
street corner acquaintance, Mr. Plotkin, who assures them that a tourist party from Pumpernickel can be
arranged for Fella and Quainto to lead. Fella and Quainto agree to meet at Plotkin's house to make
arrangements. Plotkin says he lives at 422. Given that information, will Fella and Quainto find the
house? It is unlikely. What if Plotkin says only that he lives on 4th Street? Again it is unlikely that they
will find the house. They need both the street and the house number, and of course an origin.
Figure 1
ORIGIN, OVER AND UP
Similarly, we will need two numbers
and an origin to locate a point on a graph.
We
shall call the two numbers the over number
and the up number. The origin is identified in
Figure 1 as the zero point. The over number
tells how far over, straight right, we go from
the origin. The up number tells how far
straight up we go from the origin. It does not
matter whether we go over first and then up,
or up first and then over:
we always end
at the same point. For each over and up pair,
there is one and only one point on a graph.