Linear Equation

Pronunciation: /ˈlɪn i ər ɪˈkweɪ ʒən/ ?

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

Cite this article as:


Linear Equation. 2011-04-22. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/linearequation.html.

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Revision History


2011-04-22: Added section on forms of linear equat4ions. (McAdams, David.)
2008-08-21: Added 'More Information' (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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