Question 652962
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The first thing to do is to see if the relationship is linear.  Use the slope formula and any two pairs of the first three (x, y) ordered pairs.


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


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 \ \ \ \ \ \ \ \ \ \ m_1\ =\ \frac{7\ -\ 9}{1\ -\ 2} = 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m_2\ =\ \frac{7\ -\ 13}{1\ -\ 4} = 2]


Same slope, so the points are collinear, so the function is linear.


Since it is a linear function the function can be written in the form *[tex \LARGE y\ =\ mx\ +\ b]


Substitute values:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7\ =\ m\ +\ b]


Since we already know the slope:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7\ =\ 2(1)\ +\ b]


So *[tex \LARGE b\ =\ 5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 2x\ +\ 5]


Now all you need to do is substitute the values of x for which you have no y value and do the arithmetic.


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