Graph

Pronunciation: /græf/ Explain

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:

ExampleDescription
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.

References

  1. Graph. ams.org. Geometry Glossary. American Mathematical Society. Last Accessed 8/6/2018. http://www.ams.org/featurecolumn/archive/geometry-glossary.html.
  2. Hall, H. A.. A Short Introduction To Graphical Algebra. 4th edition. www.archive.org. Macmillan and Company, Ltd.. 1907. Last Accessed 8/6/2018. http://www.archive.org/stream/shortintroductio029519mbp#page/n4/mode/1up. Buy the book
  3. Bettinger, Alvin K., Englund, John A.. Algebra and Trigonometry. pp 146-172. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/6/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n163/mode/1up. Buy the book

Educator Resources

Cite this article as:

McAdams, David E. Graph. 7/11/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/g/graph.html.

Image Credits

Revision History

7/10/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/8/2010: Added "References". (McAdams, David E.)
8/4/2008: Added types of graphs. (McAdams, David E.)
2/18/2008: Added caption to graph. (McAdams, David E.)
8/19/2007: Initial version. (McAdams, David E.)

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