F(x)=mx+b story problem

Question

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. 

Answer 1

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.