Question 242056
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What you ask cannot be done.  You cannot write "the" equation of a line that contains a given set of points.  That is because there are an infinite number of representations of such a line.  The best you can do is write "an" equation of the desired line.  Herewith the steps of procedure for writing an equation of a line through any two given points *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)].


Step 1:


Write out the two-point form for the equation of a line.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y - y_1 = \left(\frac{y_1 - y_2}{x_1 - x_2}\right)(x - x_1) ]


Where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the coordinates of the two given points.


Step 2:


Substitute the values of the given points into the general form equation.


Step 3:


Perform all indicated arithmetic and simplify the result of Step 2.


Step 4: (optional unless required by the problem instructions or instructor's directions)


Rearrange the result of Step 3 into an appropriate form, generally either slope-intercept form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ mx\ +\ b]


or Standard Form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ Ax\ +\ By\ = C]


Note:  Some texts require that A, B, and C be integers.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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