Question 608341
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The equation *[tex \LARGE y\ =\ 7] describes the set of all ordered pairs where the *[tex \LARGE x]-coordinate is any real number and the *[tex \LARGE y]-coordinate is always *[tex \LARGE 7]


So, chosing two arbitrary points from the solution set of *[tex \LARGE y\ =\ 7], use the slope formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2} ]


Choose *[tex \LARGE (x_1,7)] and *[tex \LARGE (x_2,7)] and substitute values:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{7\ -\ 7}{x_1\ -\ x_2} \ =\ 0]


regardless of the values of the *[tex \LARGE x]-coordinates.  Lines with a zero slope are horizontal.


If you have an equation of the form *[tex \LARGE x\ =\ \alpha], then the denominator of the slope formula is zero so the slope is undefined.  Lines with an undefined slope are vertical lines.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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