<PRE><B>Question 476138</B>
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You can&#39;t, at least in the sense that you cannot write &lt;i&gt;&lt;b&gt;the&lt;/b&gt;&lt;/i&gt; equation of any line.  That is because there are an infinite number of ways to express an equation of any line.  What you can do is write &lt;i&gt;&lt;b&gt;an&lt;/b&gt;&lt;/i&gt; equation of a line.


First we know that perpendicular lines have slopes that are negative reciprocals, which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_1\ \perp\ L_2 \ \ \Leftrightarrow\ \ m_1\ =\ -\frac{1}{m_2}\ \text{ and } m_1,\, m_2\, \neq\, 0]


The equation of the given line is presented in slope-intercept form, namely *[tex \Large y\ =\ mx\ +\ b].  Hence we can determine the slope of the given line simply by inspection of the coefficient on *[tex \Large x].  Take this number an calculate the negative reciprocal.


Take the slope number you just calculated and the coordinates of the origin, to wit: *[tex \Large (0,0)], and then use the two point form of an equation of a line:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ m(x\ -\ x_1) ]


where *[tex \Large \left(x_1,y_1\right)] are the coordinates of the given point and *[tex \Large m] is the calculated slope.  Put the result into whatever form your instructor expects your answers to take.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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