Question 656977
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*[tex \LARGE x] and *[tex \LARGE y]-intercepts are not numbers.  They are points.  So it is incorrect to say that the *[tex \LARGE x]-intercept is *[tex \LARGE p] and the *[tex \LARGE y]-intercept is *[tex \LARGE q].  If the *[tex \LARGE x]-coordinate of the *[tex \LARGE x]-intercept is *[tex \LARGE p], then the *[tex \LARGE x]-intercept is the point *[tex \LARGE (p,0)].  Similarly, the *[tex \LARGE y]-intercept is the point *[tex \LARGE (0,q)].


Now that you have two points, you can write an equation whose solution set is the set of ordered pairs representing the points that comprise the desired line.


Use the two-point form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ \left(\frac{y_1\ -\ y_2}{x_1\ -\ x_2}\right)(x\ -\ x_1) ]


where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the coordinates of the given points.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 0\ =\ \left(\frac{0\ -\ q}{p\ -\ 0}\right)(x\ -\ p) ]


Yours to simplify.


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