Question 635628
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What you ask cannot be done.  You defined the function *[tex \LARGE y] and then gave data about the function *[tex \LARGE f] evaluated at a couple of points.  What would you say if I took you to a concert where two new bands were playing, but I only let you listen to the first one but asked your opinion on the second one?


Be that as it may, I suspect you meant to say "consider a linear function *[tex \LARGE y\ =\ a\ +\ bx].  If *[tex \LARGE y(2)\ =\ -5], and ..."


In that case, by substitution:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b(2)\ =\ -5]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b(7)\ =\ 10]


Giving you the following 2X2 linear system:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ 2b\ =\ -5]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ 7b\ =\ 10]


Solve the system by any convenient means (it lends itself nicely to the elimination method), and once you have the values of *[tex \LARGE a] and *[tex \LARGE b] your function is fully defined.  After that, evaluating *[tex \LARGE y(-4)] is trivial.


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