Question

A spring stretches to 18 cm with a 70 g weight attached to the end. With a 100 g weight attached, it stretches to 24 cm. Which equation models the distance y the spring stretches with the weight x attached to it?

a. y = -1/5x + 4
b. y = 1/5x - 4
c. y = -1/5x - 4
d. y = 1/5x + 4

Answer 1

My guess is D y=1/5x+4

Answer 2

Answer: d.
`y=(1)/(5)x+4`

Explanation:

Let y denote the distance the spring stretches with the weight x attached to it.

Since the distance the spring stretches is directly proportional to the weight attached to it.

Therefore, the relationship between the quantities is linear.

The linear equation with points (70,18) and (24,100) is given by:-

`(y-18)=(24-18)/(100-70)(x-70)\\\Rightarrow\ y-18=(6)/(30)(x-70)\\\Rightarrow\ y-18=(1)/(5)x-14\\\Rightarrow\ y=(1)/(5)x+4`

hence, d is the right answer.

The equation models the distance y the spring stretches with the weight x attached to it is given by:-

`y=(1)/(5)x+4`