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
To find the rate of change, we can use the formula for slope:
slope = (change in y) / (change in x)
In this case, the change in y represents the change in length of the spring, and the change in x represents the change in weight attached to the spring.
Slope = (18 - 12) / (5 - 2)
Slope = 6 / 3
Slope = 2
Now that we have the slope, we can use it to find the length of the spring when no weights are attached.
Let x be the weight attached and y be the length of the spring.
y - 12 = 2(x - 2)
y - 12 = 2x - 4
y = 2x + 8
Now, substitute x = 0 (no weight attached) into the equation:
y = 2(0) + 8
y = 0 + 8
y = 8
Therefore, the length of the spring when no weights are attached is 8 inches.
The Kims are hosting a catered dinner. The cost for 3 servings is $18. The cost for 10 servings is $60. What is the cost per serving?(1 point)
$
per serving