The length of a spring is a linear function of the amount of

The length of a spring is a linear function of the amount of force in Newtons (N) exerted by weights hanging on it. For a particular spring, the length increases at the rate of 3 centimeters for each 5 Newtons of force. When a weight exerting 25 N is hung on the spring, it stretches to a length of 20 cm. Which equation relates the length of this spring, y, to the force in Newtons, x, exerted by weights hanging from it?

Solution

given length of this spring as y, the force in Newtons as x.

and length of a spring is a linear function of the amount of force in Newtons

length of a spring y =kx +c where k is slope of linear function , c is y intercept

length increases at the rate of 3 centimeters for each 5 Newtons of force

y =kx

3=k*5

==>k=3/5

y =(3/5)x +c

given When a weight exerting 25 N is hung on the spring, it stretches to a length of 20 cm

25 =(3/5)*20 +c

=> 25 =12 +c

=> c=25-12

=> c=13

y =(3/5)x +13

equation relates the length of this spring, y, to the force in Newtons, x, exerted by weights hanging from it is y =(3/5)x +13