# 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.

 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 form (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

• 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.

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.

### 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.)