Question 1087010
<font color="black" face="times" size="3">Part A) 


The two points given are


A = (x1,y1) = (0,8896)
B = (x2,y2) = (9,11965)


m = Slope of line through points A and B


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (11965 - 8896)/(9 - 0)}}}


{{{m = (3069)/(9)}}}


{{{m = 341}}}


The slope is {{{m = 341}}}.


The y intercept is {{{b = 8896}}} as this is the y value when x = 0. See point A.


So the slope intercept form {{{y = mx+b}}} turns into {{{y = 341x+8896}}} after performing substitutions or replacements.


Answer: {{{y = 341x+8896}}}


The graph looks like this


<img src="https://i.imgur.com/3qvil0E.png">


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Part B)


Plug x = 15 into the equation found in part A. Why this x value? Because 15 years have passed since 2005 to get to 2020 (2020-2005 = 15). Keep in mind that x = 0 represents the year 2005


{{{y = 341x+8896}}}


{{{y = 341*15+8896}}} x has been replaced with 15


{{{y = 5115+8896}}}


{{{y = 14011}}}


We predict that there will be about 14011 stores in the year 2020 (assuming the growth rate stays the same).


Answer: 14011


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Part C)


Slope = rise/run = (change in y)/(change in x)


The change in y is the change in the number of stores


The change in x is the change in the year number


(change in y)/(change in x) = (number of stores)/(number of years) = number of stores per year


So the slope of 341 means that Starbucks is opening 341 stores per year. In other words, there are 341 new stores opening up every year.


Obviously this pace can't keep up forever.</font>