Linear Equation

Pronunciation: /ˈlɪni.ər ɪˈkweɪ.ʒən/ Explain

A linear equation is an equation that makes a line when graphed. A linear equation can be represented by an equation in the form ax + by = c.

Figure 1 is an example of a linear equation and its graph.

Graph of the linear equation y=2x-3
Figure 1: The linear equation y = 2x - 3 and its graph.

Forms of Linear Equations

NameEquationParametersNotes
Standard form ax + by = c a, b and c All lines can be expressed in this form. This form is used in linear systems to make it easier to use matrices.
Slope-intercept form y = mx + b m is the slope, b is the y-intercept. Vertical lines can not be expressed in this form, as their slope is undefined.
Point-slope form y = m(x - x0) + y0 m is the slope of the line, (x0, y0) is the coordinate of any point on the line. This form is useful when the coordinate of a single point on the line is known along with the slope. Vertical lines can not be expressed in this form as their slope is undefined.
Two point formy = (y2-y1)/(x2-x1)(x - x1) + y1 (x1, y1) and (x2, y2) are the coordinates of two distinct points on the line. This form is useful when the coordinates of any two distinct points of a line are known. Vertical lines can not be expressed in this form as (x2 - x1) is 0, and division by zero makes the equation undefined.
Vertical linex = x0 x0 is the x-intercept. Only vertical lines can be expressed in this form.
Horizontal liney = y0 yo is the y-intercept. Only horizontal lines can be expressed in this form.
Table 1: Forms of linear equations.

References

  1. McAdams, David E.. All Math Words Dictionary, linear equation. 2nd Classroom edition 20150108-4799968. pg 108. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

  • McAdams, David E.. Line. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 8/31/2018. http://www.allmathwords.org/en/l/line.html.
  • How to Solve Simple Linear Equations in Algebra (video). dummies.com. Wiley. 8/31/2018. http://www.dummies.com/how-to/content/how-to-solve-simple-linear-equations-in-algebra.html.

Cite this article as:

McAdams, David E. Linear Equation. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/linearequation.html.

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Revision History

4/24/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/31/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
4/22/2011: Added section on forms of linear equations. (McAdams, David E.)
8/21/2008: Added 'More Information'. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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