Slope in Real-World Problems Practice

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An illustration shows three coiled wire springs stretched to varying lengths. The first spring does not have any weights pulling it downward, and the length of the spring is marked as a question mark inches. The second spring has a 2-pound weight attached to the bottom, and its length is marked as 12 inches. The third spring has a 5-pound weight attached to the bottom and its length is marked as 18 inches.

A spring has a length of 12 inches when a 2-pound weight is attached, and a length of 18 inches when a 5-pound weight is attached. Use rate of change to find the length of the spring when no weights are attached.

(1 point)
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Answer 1

To find the length of the spring when no weights are attached, we can set up a proportion using the rates of change when weights are attached:

Rate of change = (change in length of spring)/(change in weight)

For the spring with a 2-pound weight attached: (12 - x)/2 = (18 - 12)/5
For the spring with no weights attached: (x - 0)/0 = (18 - x)/5

Solving the proportion for x gives:
(12 - x)/2 = 6/5
12 - x = 12/5
x = 12 - 12/5
x = 48/5
x = 9.6

Therefore, the length of the spring when no weights are attached is 9.6 inches.

Answer 2

nope