Question 642064
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Ordered pairs are of the form *[tex \LARGE (x, y)] where *[tex \LARGE y] is a function of *[tex \LARGE x].  Had the problem asked for "price per hat as a linear function of hats sold" then your *[tex \LARGE (200,4.5)] and *[tex \LARGE (500,3.25)] ordered pairs would have been correct.  As it is, you want to reverse them, *[tex \LARGE (4.5,200)] and *[tex \LARGE (3.25,500)].


Next, you want to use the two-point form of an equation of a line:


*[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.


Plug in the values from your two points and then simplify.  Since the problem asks for a function, you want to put your equation into slope-intercept form; that is, *[tex \LARGE y\ =\ mx\ +\ b], isolating *[tex \LARGE y] to demonstrate the function relationship.


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