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Equation of a Line

The various common forms for the equation of a line are listed below. In all forms, slope is represented by m, the x-intercept by a, and the y-intercept by b.

Note: The standard form coefficients A, B, and C have no particular graphical significance.

Forms for the Equation of a Line

Slope-intercept

y = mx + b

Used when you have the slope and the y-intercept.
Point-slope

yy1 = m(xx1)

(x1, y1) is a point on the line.
Standard form

Ax + By = C

If possible, A is nonnegative and A, B, and C are relatively prime integers.
Two-intercept

Used when you have both intercepts.
Vertical

x = a

All points have x-coordinate a.
Horizontal

y = b

All points have y-coordinate b.

 

Movie Clips (with narration)

Eqn of a Horizontal Line
Horizontal Line:
how to find the equation

(1.43M)
Eqn of a Vertical Line
Vertical Line:
how to find the equation

(1.46M)
Eqn of a line, point-slope
Point and Slope:
How to find the equation of a line

(4.13M)
Eqn of a line, two points
Two Points:
How to find the equation of a line

(5.5M)

 


  this page updated 19-jul-17
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
Copyright © 2000 by Bruce Simmons
All rights reserved
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