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Algebra / Linear functions Difficulty: Medium

A team of workers has been moving cargo off of a ship. The equation below models the approximate number of tons of cargo, y, that remains to be moved x hours after the team started working.

$y equals, 120 minus 25 x$

The graph of this equation in the xy-plane is a line. What is the best interpretation of the x-intercept in this context?

The team will have moved all the cargo in about 4.8 hours.

The team has been moving about 4.8 tons of cargo per hour.

The team has been moving about 25 tons of cargo per hour.

The team started with 120 tons of cargo to move.

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Explanation

Choice A is correct. The x-intercept of the line with equation y = 120 – 25x can be found by substituting 0 for y and finding the value of x. When y = 0, x = 4.8, so the x-intercept is at (4.8, 0). Since y represents the number of tons of cargo remaining to be moved x hours after the team started working, it follows that the x-intercept refers to the team having no cargo remaining to be moved after 4.8 hours. In other words, the team will have moved all of the cargo after about 4.8 hours.

Choice B is incorrect and may result from incorrectly interpreting the value 4.8. Choices C and D are incorrect and may result from misunderstanding the x-intercept. These statements are accurate but not directly relevant to the x-intercept.