Question 198059
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If you plot the points on a graph, *[tex \LARGE x] is *[tex \LARGE x] and *[tex \LARGE f(x)] is *[tex \LARGE y], then you can see that they lie in a straight line.  


{{{drawing(
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4x + 6))}}}


So we are looking for a function that looks like:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y = f(x) = mx + b]


One of the points is (0, 6), so we can determine the value of *[tex \LARGE b] directly, since 6 is clearly the y-intercept.  So far we have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x) = mx + 6]


Now we need the value of *[tex \LARGE m]


Pick any two pairs of values (let's use (0, 6) and (1, 10)) and plug them into:


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m = \frac{6 - 10}{0 - 1} = \frac{-4}{-1} = 4]


Now we have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x) = 4x + 6]


Finally, you need to check the work.  For each pair of numbers in your table, substitute the *[tex \LARGE x] value and the *[tex \LARGE f(x)] value into the derived function.  It must result in a true statement in each case.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2 =^? 4(-2) + 6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2 =^? -8 + 6 = -2] checks.


Now, you do the rest.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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