Question 328523
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Except for a tiny error in semantics, you are spot on.  In point of fact, you cannot answer the question that was posed in the way it is posed.  "Write <i><b>the</b></i> equation of a line" is impossible.  In fact, there are an infinite number of equations that represent the set of ordered pairs for any given line.  What you wrote, and correctly, was <i><b>an</b></i> equation of the line parallel to *[tex \Large y\ =\ -3x\ +\ 1] through *[tex \Large (4,2)].


To prove that it is impossible to write the equation of a line, I only have to show that there is more than one way to write such an equation.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3kx\ +\ ky\ =\ 14k] where *[tex \LARGE k\ in\ \mathbb{R}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ ky\ =\ -3kx\ +\ 14k] where *[tex \LARGE k\ in\ \mathbb{R}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 2\ =\ \frac{12}{-4}(x\ -\ 4)]


are all representations of the same set of ordered pairs. 



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