Question

1. shipping the oocl shenzhen, one of the worlds largest container ships, carries 8063 teus (1280 - cubic - feet containers). workers can unload a ship at a rate of 1 teu every minute. the equation ( y = 8063 - 60x ) represents the number of teus on the ship y after x hours of the workers unloading the containers from the shenzhen.

a. find the x - and y - intercepts and interpret their meaning in the context of the situation.
b. graph the equation by using the intercepts.

Explanation:

Step1: Find the y - intercept

Set \(x = 0\) in the equation \(y=8063 - 60x\).
\(y=8063-60\times0=8063\).
In the context of the situation, when \(x = 0\) (i.e., at the start, 0 hours of unloading), the number of TEUs on the ship is \(8063\).

Step2: Find the x - intercept

Set \(y = 0\) in the equation \(y = 8063-60x\).

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In the context of the situation, when \(y = 0\) (i.e., when there are 0 TEUs left on the ship), it takes approximately \(134.38\) hours to unload all the containers.

Answer:

a. The \(y\) - intercept is \((0,8063)\) (initial number of TEUs on the ship). The \(x\) - intercept is \((\frac{8063}{60},0)\approx(134.38,0)\) (time to unload all TEUs).
b. To graph the equation using the intercepts:

• Plot the \(y\) - intercept \((0,8063)\).
• Plot the \(x\) - intercept \((\frac{8063}{60},0)\approx(134.38,0)\).
• Draw a straight line passing through these two points. Since \(x\geq0\) (time cannot be negative) and \(y\geq0\) (number of TEUs cannot be negative), we consider the part of the line in the first quadrant.