Question

Nadia is placing different weights on a spring and measuring the length of the stretched spring. She finds that for a 100 gram weight the length of the stretched spring is 20 cm and for a 300 gram weight the length of the stretched spring is 25 cm. write an equation in point slope form that describes this situation. What is the unstretched length of the spring?

Answer 1

`y-20=(1)/(40)(x-100)`

Explanation:

Slope formula:

100 grams would be an x(1) coordinate

20 cm would be a y(2) coordinate

300 grams would be an x(2) coordinate

20 cm would be a y(2) coordinate

They would be written like this: (100,20), (300,20)

You would use the slope formula to find m

`(y(2) - y(1))/(x(2)-x(1))`

Slop-point formula: y-y(1)=m(x-x(1))

When slope is solved, you get 1/40

When solved for slope-point, y - 20 = 1/40 (x-100)

Answer 2

The first thing to recognize that if an equation is in point slope form( y-y1=m(x-x1)) it is a linear equation. Furthermore, because it is in point slope form, the only thing you need to find the equation are the coordinates of two points, which you have: (100, 20) and (300, 25).
First find the m (slope). Do this by completing the formula: (y1-y2)/(x1-x2). In this case, plug in (25-20)/(300-100). When you solve, the answer becomes .025. Then all you need is one of the points to finish the formula.
Thus, the answer becomes y-20=.025(x-100)