Pronunciation: /græf/ ?

A graph is a visual representation of an algebraic relationship.

Graph of the line y=2x-1
Figure 1: Graph of the line y = 2x-1

When we draw a graph, we are drawing a representation of a relationship such as y = 2x - 1. A graph can help us understand and interpret an algebraic relationship.

Types of Graphs

Number Lines

A number line is a one dimensional graph. Examples of number lines include:

Number line with solid dot on 5 labeled ANumber line showing A=5.
Number line with solid dot on -3 and an arrow going to the left labeled B.Number line showing B≤-3.
Number line with solid dot on -5, a hollow dot on 2.5, and a segment connecting the two dots labeled C.Number line showing -5 ≤ C < 2.5.
Number line with hollow dot on 0 and an arrow going to the left from 0, a solid dot on 3, and an arrow going to the right from 3.Number line showing D < 0 or D ≥ 3.
Table 1: Examples of number lines.

Graphs Using Cartesian Coordinates in 2 Dimensions

Graph of y=x^2-4
Figure 1: Graph of y = x2-4.

When graphing a relationship between two variables, one usually uses a 2-dimensional Cartesian coordinate system.


  1. graph. WordNet. Princeton University. (Accessed: 2011-01-08).
  2. Graph. Geometry Glossary. American Mathematical Society. (Accessed: 2010-02-05).
  3. Hall, H. A.. A Short Introduction To Graphical Algebra, 4th ed.. Macmillan and Company, Ltd., 1907. (Accessed: 2010-02-08).
  4. Bettinger, Alvin K., Englund, John A.. Algebra and Trigonometry, pp 146-172. International Textbook Company, January 1963. (Accessed: 2010-02-08).

Educator Resources

Printed Resources

Cite this article as:

Graph. 2010-02-08. All Math Words Encyclopedia. Life is a Story Problem LLC.


Image Credits

Revision History

2010-02-08: Added "References" (McAdams, David.)
2008-08-04: Added types of graphs (McAdams, David.)
2008-02-18: Added caption to graph (McAdams, David.)
2007-08-19: Initial version (McAdams, David.)

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