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Slope-Intercept Form (page 2)

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Updated on Feb 18, 2014

How to Find the Equation of a Line When From Two Points

  1. Calculate the slope of the line.
  2. Plug the slope into y = mx + b.
  3. Plug in the x- and y-values from one of the two given points.
  4. Solve for b.

 

Example 1:

Find the equation of the line containing points A: (4, 1) and B: (2, 3).

  1. [3 - (-1)] / (2 - 4) = 4 / -2 = -1.
  2. y = -x + b
  3. (3) = -(2) + b
  4. b = 5

​Solution: y = -x + 5

 

Example 2:

Find the equation of the line containing (⅔, 4) and (-12, -.25).

  1. [4 - (-.25)] / [⅔ - (-12)] = 4.25 / 12.67 = .335
  2. y = .335b
  3. (4) = .335 (⅔) + b
  4. 4 = .224 + b = 3.776

Solution: = .335+ 3.776

 

Other Ways to Express a Linear Equation

Standard Form:

standard form

Example 1: 

2+ 5= 20

a = 2, b = 5, c = 20

Example 2:

-x/2 - 5y/3 = 12

a = -12, b = -53, c = 12

Point-Slope Form:

point-slope form

Example 1: 

An equation of a line with a slope of 2 that intersects the point (4, 5): 

- 5 = 2(- 4)

Example 2:

An equation of a line with a slope of -23 that intersects the point (-2, -1): ​

- (-1) = (-23(x - (-2) )

+ 1 = -23(x + 2)

David Travis is the founder and CEO of Prospect Prep, a New York City-based tutoring agency dedicated to helping students earn better grades, higher scores, and acceptance letters from the colleges of their dreams.

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