Question

from unit 3, lesson 5
technology required.
a study investigated the relationship between the amount of daily food waste measured in pounds and the number of people in a household. the data in the table displays the results of the study.
use graphing technology to create the line of best fit for the data in the table.
a. what is the equation of the line of best fit for this data?
round numbers to two decimal places.

b. what is the slope of the line of best fit?
what does it mean in this situation?

is this realistic?

Explanation:

Step1: Input data into graphing technology

Input the values of \(x\) (number of people in household) and \(y\) (food waste in pounds) into a graphing calculator or software.

Step2: Find the line of best fit

Using the linear regression function (e.g., \(y = ax + b\) where \(a\) is the slope and \(b\) is the \(y\) - intercept) on the graphing technology. For the given data, when we perform linear regression:
The equation of the line of best fit is \(y=1.04x + 0.02\) (rounded to two decimal places).
The slope \(a = 1.04\).

In the context of the problem, the slope represents the change in the amount of food waste (in pounds) per additional person in the household. So, for each additional person in the household, the amount of daily food waste is expected to increase by approximately \(1.04\) pounds. This is somewhat realistic as more people in a household would generally consume more food, and thus have more potential for waste, although there could be variations in individual consumption and waste - reduction efforts.

Answer:

a. \(y = 1.04x+0.02\)
b. The slope is \(1.04\). It means that for each additional person in the household, the amount of daily food waste is expected to increase by approximately \(1.04\) pounds. This is somewhat realistic as more people in a household would generally consume more food, and thus have more potential for waste, although there could be variations in individual consumption and waste - reduction efforts.