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F(x)=mx+b story problem

A store holds birthday parties for kids. They charge a party fee plus a fee for each guest. If there are 10 guests it cost $105 while if there are 25 guests it cost $210. Find a f(x) =mx+b where the input  x is the # of guests and the output f(x) is the cost of the party. 
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1 Answer

You have two points on the line: (10,105) and (25,210).  That's all you need to find the equation of the line y = mx + b where m is the slope and b is the y-intercept.
 
The slope of the line, m, is the change in y over the change in x between the two points:
 
m = (210-105)/(25-10) = 105/15 = 7
 
So far our equation is:
 
y = 7x + b
 
To find b, plug either point into the equation.  I'll use (10,105):
 
105 = 7(10) + b
 
105 = 70 + b
 
35 = b
 
y = 7x + 35
 
The party fee is $35 and the charge per guest is $7.