Point-Slope Form of the Equation of a Line

What: The equation of a line with slope m through the point (x1, y1 ).

Form: y - y1 = m(x - x1 )

Can use when: How to use:
Given a point and a slope Just plug in the given slope m and the given point (x1, y1 )
Given two points
  1. Calculate the slope m
  2. Plug in the calculated slope m and either of the given points for (x1, y1 )

Slope-Intercept Form of the Equation of a Line

What: The equation of a line with slope m and y-intercept (0, b).

Form: y = mx + b

Can use when: How to use:
Given the slope and the y-intercept Just plug in the given slope m and b which is the y-coordinate of the y-intercept
Given a point and a slope
  1. Plug in the given slope m and the given point for (x, y).
  2. Solve for b.
  3. Plug in the slope m and b to write as y = mx + b.
Given two points
  1. Calculate the slope m
  2. Now do same as for "Given a point and a slope."

General Form of the Equation of a Line

What: Any equation of a line can be algebraically manipulated to get it to this form.

Form: Ax + By + C = 0, where A, B, and C are integers.




Creator: CJ Kentler
kentler@delta.math.wsu.edu
Washington State University
Department of Mathematics
Pullman, Wa. 99164-3113
1997