Question 326105
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Recall the slope formula: The difference in the *[tex \LARGE y]-coordinates  divided by the difference in the *[tex \LARGE x]-coordinates.


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


In order for the line to be vertical, *[tex \LARGE x]-coordinates have to be equal.  If the *[tex \LARGE x]-coordinates are equal, the denominator (the difference in the *[tex \LARGE x]-coordinates) has to be zero. If the denominator is zero, the slope is undefined.  So a vertical line has an undefined slope and is a set of ordered pairs where all of the *[tex \LARGE x]-coordinates are identical.  If you want your vertical line to pass through the point *[tex \LARGE (4,-7)], then all of the points on your line must have an *[tex \LARGE x]-coordinate of 4, and you don't care what the *[tex \LARGE y]-coordinate value is.  The only way to describe such a set of ordered pairs is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 4]


Which, if you consider the possibility of writing it as:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 0y\ =\ 4]


is, as you can see, written in Standard Form.  The equation of a vertical line is the only equation of a line that CANNOT be written in slope-intercept, point-slope, or two-point form because all of these forms require expressing the slope.


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