The relation between the cost of a certain gem and its weight is linear.

Question

The relationship 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 $3549, while the other gem weighs 0.7 carat and costs $4375.

Answer 1

The linear relationship between weight in carats and and cost in dollars is given by the slope of the line from 

 

(0.4 carats, $3549) to (0.7 carats, $4375)  

 

The slope is given by (Change in Y) / (Change in X) which is 

 

($4375 - $3549) / (0.7 carats - 0.4 carats) = $826 / 0.3 carats = $2753.33 per carat