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Question 534161: The cost for hosting a dinner party at a restaurant are as follows, write a linear equation to represent the cost, and find the cost for 100 people
people cost
10 300
20 400
50 700
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! We can look at these as (x,y) pairs.
(10,300)
(20,400)
(50,700)
.
We can use two of the pairs to define a straight line and then use the third point to force the line go through the third point.
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m = slope = change in y / change in x
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300-400 = -100
20-10 = -10
m = 10
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y = 10x + b
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700 = 10(50) +b
b = 700-500 = 200
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y = 10x + 200
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That means the total cost for the dinner party is $200 + $10 per person.
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So, x=100 leads us to forecast the total cost = 200 + 10*100 = $1200
.
Done.
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