Question

A spring stretches to 22 cm with a 70 g weight attached to the end. With a 105 g weight attached, it stretches to 27 cm. Which equation models the distance y the spring stretches with weight x attached to it?

Answer 1

simple form of the equation y= ax+b
y= (1/7)x + 12
come from 2 equation :
22= 70 a + b
27= 105 a + b

Answer 2

`y=(1)/(7)x+12`

Explanation:

Let y represent the distance the spring stretches and x be the weight attached to the spring.

We have been given that a spring stretches to 22 cm with a 70 g weight attached to the end. With a 105 g weight attached, it stretches to 27 cm.

First of all, we will find slope of line using the points (70,22) and (105,27) as shown below:

`m=(y_2-y_1)/(x_2-x_1)`

`m=(27-22)/(105-70)`

`m=(5)/(35)`

`m=(1)/(7)`

Now, we will substitute
`m=(1)/(7)` and coordinates of point (70,22) in slope-intercept form of equation to find the y-intercept for our equation.

`y=mx+b`

`22=(1)/(7)*70+b`

`22=1*10+b`

`22=10+b`

`22-10=10-10+b`

`12=b`

Upon substituting
`b=12` and
`m=(1)/(7)` in slope-intercept form of equation we will get our required equation as:

`y=(1)/(7)x+12`

Therefore, the equation
`y=(1)/(7)x+12` models the distance y the spring stretches with weight x attached to the spring.