Question 200615
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First determine the slope (*[tex \Large m_1]) of the line: *[tex \Large y = 2].


Then use the fact that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_1 \parallel L_2 \ \ \Leftrightarrow\ \ m_1 = m_2]


to determine the slope of the desired line.


Then use the slope of the desired line (*[tex \Large m_2]) and the given point *[tex \Large \left(x_1,y_1\right) = \left(7,12\right)]in the point-slope form of the equation of a line to derive the desired equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y - y_1 = m_2(x - x_1) ]


However, please note that you cannot write "the" equation of any line.  You can only write "an" equation of a line (or several equations of the line, if that is something you enjoy doing).  In the first place, you could just substitute the values in the point-slope form and have an equation of the desired line, or you could solve for *[tex \Large y] to put it into slope-intercept form, or you could rearrange it into standard form, namely *[tex \Large Ax + By = C].  Furthermore, for a given *[tex \Large A], *[tex \Large B], and *[tex \Large C], *[tex \Large kAx + kBy = kC] where *[tex \Large k\ \in\ \R] describes a set of equations with an infinite number of elements, each of which graphs to the same line in *[tex \Large \R^2].


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