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What is equation of line AB if A(-1,1)B(3,7)?

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luvgoj | Student, Undergraduate | Honors

Posted July 15, 2013 at 3:03 PM via web

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What is equation of line AB if A(-1,1)B(3,7)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 15, 2013 at 3:17 PM (Answer #1)

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There exists more formulas available to write the equation of a line. You need to select one formula depending on information provided by the problem, such that:

`(AB): y - y_A = (y_B - y_A)/(x_B - x_A)(x - x_A)`

Replacing the corresponding values of coordinates in equation yields:

`(AB): y - 1 = (7 - 1)/(3 - (-1))(x - (-1))`

`(AB): y - 1 = (6/4)(x + 1)`

`(AB): y - 1 = (3/2)(x + 1) => (AB): 2y - 2 = 3x + 3`

`(AB): 3x - 2y + 3 + 2 = 0 => (AB): 3x - 2y + 5 = 0`

Hence, evaluating the equation of the line (AB), under the given conditions, yields ` (AB): 3x - 2y + 5 = 0.`

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academicsfirst | High School Teacher | (Level 2) Adjunct Educator

Posted July 15, 2013 at 5:30 PM (Answer #2)

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Another approach to use to find the equation is as follows:

Step 1:  Find the slope:   m = 7 - (1)/ 3-(-1)

                                      m = 3/2

Step 2: Substitute slope and either of the given points into the slope-intercept form.  We'll use the point (3,7).  Solve for "b" which is the y intercept.

                 y = mx + b

                 7 = 3/2(3) + b

                 7 = 9/2 + b

                 5/2 = b

Step 3:  Substitute the slope which is 3/2 and the y intercept which is 5/2 into the slope intercept form.

                 Answer:  y = 3/2x + 5/2

Slope intercept form makes the equation easy to graph!

 

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