3.1

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 0.2 carat and costs $3542, while the other gem weighs 0.4 carat and costs $4380. Complete parts (a) through (d) below. (a) Find a linear equation that relates the price of a gem, y, to its weight, x. (Simplify your answer. Use integers or decimals for any numbers in the equation.) (b) Predict the price of a gem that weighs 0.75 carat. The price of a diamond is $]. (Round to the nearest cent as needed.) (c) Interpret the slope as a rate of change in the context of the problem. Choose the correct answer below. O A. If the price increases $1, the weight increases 4190 carat. O B. If the weight increases 1 carat, the price increases $2704.00. O C. If the weight increases 1 carat, the price increases $4190.00. O D. If the price increases $1, the weight increases 2704 carat. (d) If a gem costs $6600.70, what should it weigh? The weight of the gem is carat. (Round to two decimal places as needed.)