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)
To find the rate of change, we can use the formula:
Rate of change = (change in y) / (change in x)
In this case, the change in weight is 5 - 2 = 3 pounds, and the change in length is 18 - 12 = 6 inches.
Therefore, the rate of change is:
Rate of change = 6 / 3 = 2 inches per pound
To find the length of the spring when no weights are attached, we can use the rate of change formula. Since the weight is 0 pounds, the change in weight is 0 - 2 = -2 pounds.
Using the rate of change formula:
Change in length = Rate of change * Change in weight
Change in length = 2 * (-2) = -4 inches
So, the length of the spring when no weights are attached is 12 inches - 4 inches = 8 inches.