Question 242329
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Technically, you cannot do what you ask.  You cannot write "the" equation of a line.  The set of equations that represent a given line has an infinite number of elements.  You can, however, derive an equation which solution set is a set of ordered pairs that represent a straight line in *[tex \Large R^2].


First re-arrange the given equation so that it is in slope-intercept form, i.e. *[tex \Large y\ =\ mx\ +\ b].  Then determine the slope of the given line by inspection.  Take the negative reciprocal of the slope of the given line as the slope of the desired line because:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = -\frac{1}{m_2} \text{ and } m_1, m_2 \neq 0]


Using the slope determined from the previous step and the coordinates of the given point, apply the point-slope form of an equation of a line:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y - y_1 = m(x - x_1) ]


Where *[tex \Large m] is the derived slope and *[tex \Large \left(x_1,y_1\right)] are the coordinates of the given point.


Rearrange the equation into standard form, namely:


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


Some texts require that A, B, and C be integers for proper standard form.


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