Question 646229
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Notice that there is a constant difference in the input values from one to the next.  There is also a constant difference in the output values form one to the next.  Therefore, the relation is linear.


Create two ordered pairs *[tex \LARGE (Input,Output)] using the data given.  It doesn't matter which of the pairs 0,5 4,7  8,9 or 12,11 that you pick as long as you have two of them.


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.


Do the arithmetic and simplify.  Since you are asked for a function rule, you need to solve the equation for *[tex \LARGE y] in terms of everything else.  That is, you want to put your equation into slope-intercept form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ mx\ +\ b]


That way the function relationship between the *[tex \LARGE x] (Input) values and the *[tex \LARGE y] (Output) values is clearly established.


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