Slope in Real-World Problems Practice
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Question
Use the image to answer the question.
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)
inches
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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.