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October 19th, 2017, 12:21 PM  #1 
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  A small business owner has determined that the cost to produce 12 tables in a month
hello people I was able to find the 875 but I am not sure where the 2500 comes from..thanks for the help! c(n)=875n+2500 
October 19th, 2017, 12:37 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422 
you have two ordered pairs ... (number of tables, cost) $(12,13000)$ and $(22,21750)$ $C13000 = \left(\dfrac{2175013000}{2212}\right) (N  12)$ simplify ... 
October 19th, 2017, 01:07 PM  #3 
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  okay thanks I would have never guessed to set it up that way so thanks! just wondering for where you but (N12) that could have also been (N22) or is that a no 
October 23rd, 2017, 10:51 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
Frankly, the question, as given "Find a formula linear function that models the number of tables made in a month, C, if the number of tables made is n" makes no sense! This is apparently a translation into English of a problem that was not initially in English so I can forgive the awkward "formula linear function" but taking this literally, the answer would be "C(n)= n" but you and everyone who responded here has correctly interpreted this to say "models the cost of the tables made in a month, C, if the number of tables is n". You want the equation of the line that passes through (x, y)= (12, 13000) and (x, y)= (22, 21750). You should know that any linear function can be written in the form y= ax+ b. With x= 12 and y= 13000 that is 13000= 12a+ b. With x= 22 and y= 21750, 21750= 22a+ b. Subtracting the first equation from the second, 8750= 10a, a= 8750/10= 875. Putting that value of a into 13000= 12a+ b gives 13000= 12(875)+ b, 13000= 10500+ b, b= 13000 10750= 2500. 
October 25th, 2017, 10:55 AM  #5  
Math Team Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422  Quote:
$(x_1,y_1) = (12,13000)$, $(x_2,y_2) = (22,21750)$ $m = \dfrac{y_2y_1}{x_2x_1} = \dfrac{2175013000}{2212} = 875$ or ... $m = \dfrac{y_1y_2}{x_1x_2} = \dfrac{1300021750}{1222} = 875$ pointslope form of a linear equation ... $y  y_1 = m(x  x_1)$ $y  13000 = m(x  12)$ or ... $y  y_2 = m(x  x_2)$ $y  21750 = m(x  22)$ ... if you use $y_1$, you need to use $x_1$; same idea with $y_2$ and $x_2$. Either way, you'll wind up with the same final equation.  

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