Question 1018101
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The two points you are given are *[tex \Large \left(2,\,225\right)] and *[tex \Large \left(5,\,480\right)].


Part A:  Use the two-point form to derive an equation for the line that passes through your two points.


*[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.


Rearrange this equation into standard form, namely:  *[tex \Large Ax\ +\ By\ =\ C]  Note: Some instructors demand that *[tex \Large A, B] and *[tex \Large C] be integers and that *[tex \Large A] be non-negative.


Part B:  Solve the equation of part A for *[tex \Large y] in terms of everything else, so that you have the slope-intercept form *[tex \Large y\ =\ mx\ +\ b].  Then replace *[tex \Large y] with *[tex \Large f(x)]


Part C:  The easiest way is to plot the two points given at the start of the discussion and draw a straight line through them.  Use a reasonable interval for the domain of your function.  Ask yourself questions like, "is it reasonable that Sam would rent the boat for a negative number of days?" or "would Sam be likely to pay a rental fee that would be in excess of what purchase price of the boat would be?" (to get an idea of the maximum number of days he might rent the boat).  You might want to specify that the function is defined over the integers.  While it is possible that the owner of the boat might have a granularity of half-days, he certainly wouldn't rent it for say, the square root of 2 days.


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

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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