Question

laura bought a roll of string to make friendship bracelets. she makes each bracelet the same length. the amount of string laura has left depends on how many bracelets she has made. there is a linear relationship between the number of bracelets laura makes and the amount of string she has left, in meters. describe the rate of change for this relationship. the amount of string left dropdown by dropdown per bracelet.

Explanation:

Step1: Identify two points on the line

We can see from the graph that when the number of bracelets (\(x\)) is \(0\), the amount of string left (\(y\)) is \(40\) meters (the y - intercept). When \(x = 50\), \(y=0\) meters.

Step2: Calculate the rate of change (slope)

The formula for the slope \(m\) of a line between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,40)\) and \((x_2,y_2)=(50,0)\). Then \(m=\frac{0 - 40}{50 - 0}=\frac{- 40}{50}=-\frac{4}{5}=- 0.8\). The negative sign indicates that the amount of string left is decreasing. The magnitude of the slope (\(0.8\) or \(\frac{4}{5}\)) tells us the rate of decrease per bracelet.

Answer:

The amount of string left \(\boldsymbol{\text{decreases}}\) by \(\boldsymbol{0.8}\) (or \(\boldsymbol{\frac{4}{5}}\)) meters per bracelet.