Question

there is a linear relationship between the mass of an object attached to a vertical spring and the length of the spring extension. the table shows data collected after certain objects were each attached to the spring.

what is the length of the spring extension, in centimeters, when a 70 - gram object is attached to the spring?

17.5
24.5
38.5
49

Explanation:

Step1: Find the slope (m)

Using points \((40, 14)\) and \((90, 31.5)\),
\(m = \frac{31.5 - 14}{90 - 40} = \frac{17.5}{50} = 0.35\)

Step2: Determine the linear equation

Using \((40, 14)\) and \(m = 0.35\):
\(14 = 0.35(40) + b\)
\(14 = 14 + b \implies b = 0\)
Equation: \(y = 0.35x\)

Step3: Calculate extension for 70 grams

Substitute \(x = 70\) into \(y = 0.35x\):
\(y = 0.35(70) = 24.5\)

Answer:

B. 24.5