Question

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?
c. what is the y - intercept 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) into a graphing calculator or software (e.g., Desmos).

Step2: Find the line of best fit

Using the linear regression function in the graphing technology. For a set of data points \((x_i,y_i)\), the line of best fit is of the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
Let's assume we use a graphing calculator (TI - 84 or similar). After entering the data:

• For part (a):

The line of best fit equation (using linear regression) is \(y=1.17x - 0.73\) (values may vary slightly depending on the technology's algorithm precision, but after rounding to two decimal places).

• For part (b):

The slope \(m = 1.17\). In this situation, the slope represents the change in the amount of food waste (in pounds) per additional person in the household. Since as the number of people in a household increases, we would expect the amount of food waste to increase (more people eat, more potential waste), a positive slope is realistic.

• For part (c):

The \(y\) - intercept \(b=- 0.73\). The \(y\) - intercept represents the amount of food waste when there are \(x = 0\) people in the household. A negative \(y\) - intercept is not realistic in the context of food waste because if there are \(0\) people in the household, there should be \(0\) (or non - negative) food waste.

Answer:

a. \(y = 1.17x-0.73\)
b. The slope is \(1.17\). It means that for each additional person in the household, the amount of food waste increases by approximately \(1.17\) pounds. Yes, it is realistic.
c. The \(y\) - intercept is \(-0.73\). It means the amount of food waste when there are \(0\) people in the household. No, it is not realistic.