A quarry runs a delivery service for cut stone. The cost to deliver the stone is a flat fee for the delivery plus the cost of the stone in terms of weight. The graph of the total cost C, in dollars as a function of the weight, x, in pounds of the cut stone is shown. What is the meaning of the y-intercept?
The y-intercept of the graph represents the total cost when the weight of the cut stone is 0 pounds. In this context, it means that even if there is no stone to be delivered (weight is 0), there is still a flat fee for the delivery.
The y-intercept of a graph represents the value of the dependent variable (in this case, the cost) when the independent variable (in this case, the weight) is equal to zero. In the context of this problem, the y-intercept of the graph of the total cost C represents the cost (in dollars) when the weight of the cut stone is zero pounds, or in other words, when no stone is delivered. This y-intercept value would likely represent the flat fee for the delivery service.
To find the meaning of the y-intercept in the graph, we need to understand the relationship between the variables involved. In this case, the graph represents the total cost (C) of delivering cut stone based on its weight (x) in pounds.
The y-intercept is the point where the graph intersects the y-axis, which occurs when the weight of the stone is zero. This means that no stone is being delivered.
The y-intercept represents the fixed cost or the flat fee for the delivery service. It is the amount of money that needs to be paid even if there is no stone being delivered. It covers expenses such as operating costs, labor, or any other associated costs with the delivery service, regardless of the weight of the stone.
Therefore, the y-intercept in this context signifies the base cost of delivery, which is independent of the weight of the stone being delivered.