A physics lab group conducted an experiment to determine the length of a spring when different objects of varying weight were hung from it. After testing ten different objects, the group calculated the following linear regression, where \( x \) is the weight of the object in ounces and \( h(x) \) is the length of the spring in centimeters:
\[ h(x) = 2.3x + 15.5 \]
What does the y-intercept of this equation indicate about the relationship between object weight and the length of the spring?
1. When there is no object on the spring, its length is 2.3 cm.
2. When there is no object on the spring, its length is 15.5 cm.
3. For every ounce of weight, the spring length increases by 2.3 cm.
4. For every ounce of weight, the spring length increases by 1535 cm.
Answer (3)
2). The length of the spring is 15.5 cm, and that's how it hangs when there's no weight on it.
In the equation, 'x' is the weight of the object. If there's no object, then x = 0 and h(x) = 15.5 .
15.5 is the answer man...that was pretty hard
The y-intercept of the equation h ( x ) = 2.3 x + 15.5 indicates that when no weight is applied, the length of the spring is 15.5 cm. This means that the spring starts at this length without any objects hanging from it. Therefore, the correct answer is option 2.
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