Two Dimensional (x-y) Graphing

The relationship between any two properties of a system can be represented graphically by a two-dimensional data plot. Such a graph has two axes: a horizontal one corresponding to the independent variable, or the variable whose value is being controlled (x), and a vertical axis corresponding to the dependent variable, or the variable whose value is being observed or measured (y).

When the value of y is changing as a function of x (that is, different values of x correspond to different values of y), a graph of this change can be plotted or sketched. The graph can be produced by using specific values for (x,y) data pairs.

Graphing the Dependence of y on x

xy
15
210
37
414
Sample data for making an x-y plot

This table contains the following points: (1,5), (2,10), (3,7), and (4,14). Each of these points can be plotted on a graph and connected to produce a graphical representation of the dependence of y on x.

A graph is titled “Dependency of Y on X.” The x-axis ranges from 0 to 4.5. The y-axis ranges from 0 to 16. Four points are plotted as a line graph; the points are 1 and 5, 2 and 10, 3 and 7, and 4 and 14.

If the function that describes the dependence of y on x is known, it may be used to compute x,y data pairs that may subsequently be plotted.

Plotting Data Pairs

If we know that y = x2 + 2, we can produce a table of a few (x,y) values and then plot the line based on the data shown here.

xy = x2 + 2
13
26
311
418
Data for plotting the graph of x2 + 2
A graph is titled “Y equals x superscript 2 plus 2.” The x-axis ranges from 0 to 4.5. The y-axis ranges from 0 to 20. Four points are plotted as a line graph; the points are 1 and 3, 2 and 6, 3 and 11, and 4 and 18.