SOLUTION: The relation between the cost of a certain gem and its weight is linear. In looking at two​ gems, we find that one of the gems weighs 0.4 carat and costs ​$3543​,
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Question 1086062: The relation between the cost of a certain gem and its weight is linear. In looking at two gems, we find that one of the gems weighs 0.4 carat and costs $3543, while the other gem weighs 0.6 carat and costs $4375.
(a) Find a linear function that relates the price of a gem, C(x), to its weight, x, treating weight as the independent variable.
(b) Predict the price of a diamond that weighs 0.73 carat.
(c) Interpret the slope, and choose the correct answer.
A. If weight increases 1 carat, price increases $1879.
B. If price increases $1, weight increases 1879 carat.
C. If price increases $1, weight increases 4160 carat.
D. If weight increases 1 carat, price increases $4160.
(d) If a diamond costs $5706.20, what do you think it should weigh?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Weight is x (independent variable)
Cost is y (dependent variable)
slope is (4375-3543)/(0.6-0.4)=832/0.2=$4160/carat
point slope formula y-y1=m(x-x1), where m slope and (x1,y1) point
y-4375=4160(x-0.6)
y-4375=4160x-2496
a)y=4160x+1879
b) y=4160(0.73)+1879=3036.80+1879=$4915.80
c)For every increase of 1 carat, the price increases $4160.
D.
d)5706.20=4160x+1879
3827.2=4160x
x=0.92 carats
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