Question

A store offers packing and mailing services to customers. If a customer ships a box weighing 3 pounds, it would cost $12. If a customer ships a box weighing 9 pounds, it would cost $36. Identify the following characteristics:

What is the input?
What is the output?
What is the slope?
What does the slope represent?
What is the y-intercept?
What does the y-intercept represent in words?

Answer 1

In the mailing service cost scenario, the input is the weight of the box, the output is the cost to ship, the slope is $4 per pound representing the cost per additional pound, and the y-intercept (not provided) would theoretically be a flat service fee.

Step-by-step explanation:

For the scenario where a store offers packing and mailing services with costs based on weight, the following characteristics can be identified:

• The input is the weight of the box in pounds.
• The output is the cost of shipping the box in dollars.
• The slope can be calculated by taking the change in cost divided by the change in weight. Using the two given points (3, $12) and (9, $36), the slope is ($36 - $12) / (9 - 3) = $24 / 6 = $4 per pound.
• The slope represents the rate at which costs increase with each additional pound of weight.
• To find the y-intercept, we would need additional information, such as the cost for shipping a box weighing 0 pounds. In most scenarios like this, the y-intercept would represent a minimum or base charge for shipping.
• Without an actual y-intercept value given, we can speculate that the y-intercept represents a flat service fee that applies regardless of weight, if any such fee exists.