Question

at sunshine citrus co., workers take oranges from a large bin and pack them into smaller boxes for shipment to grocery stores. the bin gets lighter as the boxes are packed. this situation can be modeled as a linear relationship. chart: x-axis boxes packed (5,10,15,20,25,30,35,40,45,50), y-axis bins weight (pounds) (100,200,300,400,500,600,700,800,900,1000), line from (0,700) to (50,200) what does the slope of the line tell you about the situation?

Explanation:

Step1: Identify two points on the line

From the graph, we can see that when \( x = 0 \) (no boxes packed), \( y = 700 \) pounds (initial bin weight). When \( x = 50 \) (50 boxes packed), \( y = 200 \) pounds (bin weight after 50 boxes).

Step2: Calculate the slope

The formula for slope \( m \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \( (x_1,y_1)=(0,700) \) and \( (x_2,y_2)=(50,200) \). Then \( m=\frac{200 - 700}{50 - 0}=\frac{- 500}{50}=- 10 \).

Step3: Interpret the slope

The slope is - 10. In the context of the problem, the \( x \)-axis represents the number of boxes packed and the \( y \)-axis represents the bin's weight. A slope of - 10 means that for each additional box packed (increase in \( x \) by 1), the bin's weight ( \( y \)) decreases by 10 pounds.

Answer:

The slope of - 10 tells us that for each box of oranges packed, the weight of the bin decreases by 10 pounds.