Linear Equation

Pronunciation: /ˈlɪn i 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 formax + by = ca, b and cAll lines can be expressed in this form. This form is used in linear systems to make it easier to use matrices.
Slope-intercept formy = mx + bm is the slope, b is the y-intercept.Vertical lines can not be expressed in this form, as their slope is undefined.
Point-slope formy = m(x - x0) + y0m 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 = x0x0 is the x-intercept.Only vertical lines can be expressed in this form.
Horizontal liney = y0yo is the y-intercept.Only horizontal lines can be expressed in this form.
Table 1: Forms of linear equations.

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. 8/31/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/linearequation.html.

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Revision History

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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