Question 895979
Each time you're adding 3 (5 to 8, 8 to 11)


So the rate of change is 3 people per table, which represents the slope.


So m = 3/1 = 3


Let x = number of tables, y = number of people


"1 table seats 5 people" means x = 1, y = 5



y = mx+b


y = 3x+b


5 = 3*1+b


5 = 3+b


5-3 = b


2 = b


b = 2


So the model is y = 3x+2


Notice how if we have 3 tables for instance, then x = 3


y = 3x+2


y = 3*3+2


y = 11


which reflects the fact "3 tables seat 11 people"


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If we have 39 people, then y = 39. Let's find x


y = 3x+2


39 = 3x+2


39-2 = 3x


37 = 3x


3x = 37


x = 37/3


x = 12.3333...


Round that up to go from 12.3333.... to 13


You'll need 13 tables. Twelve of those tables will have 3*12+2 = 38 people and that last table (the thirteenth table) will have 39-38 = 1 person. 


Of course, you can move people around and have the structure of some tables different, but overall you need 13 tables.


If she had just 12 tables, then one person would be left out.