Question

algebra 1
unit 3
lesson 6 practice
name_
date_
period_
use this scenario for questions 1 through 6. polly sells hot chocolate at a stand in a
park. she records the number of cups of hot chocolate she sells, as well as the average
daily low temperature. the table shown indicates the data for 12 days in january.
hot chocolate sales

polly used technology to generate a scatter plot and a line of best fit, as shown.

1. write the equation for the line of best fit using the values generated with

technology.

1. interpret the slope of the line of best fit in the context.

describe the strength of the association between temperature and the number of
cups of hot chocolate polly sells.

Explanation:

Step1: Write the equation of the line of best fit

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. From the given parameters \(m=-1.81319\) and \(b = 171.387\). So the equation is \(y=-1.81319x + 171.387\)

Step2: Interpret the slope

The slope \(m=-1.81319\). In the context of the problem, \(x\) is the average temperature (\(^{\circ}F\)) and \(y\) is the number of cups of hot chocolate sold. The slope represents the rate of change. So, for every 1 - degree increase in temperature, the number of cups of hot chocolate sold decreases by approximately \(1.81\) cups.

Step3: Describe the strength of the association

The correlation coefficient \(r=-0.8861\). Since \(|r|\) (where \(|r| = 0.8861\)) is close to \(1\) (\(0.8<|r|<1\)), there is a strong negative linear association between the average temperature and the number of cups of hot chocolate sold.

Answer:

1. The equation of the line of best fit is \(y=-1.81319x + 171.387\)
2. For every 1 - degree increase in temperature, the number of cups of hot chocolate sold decreases by approximately \(1.81\) cups.
3. There is a strong negative linear association between temperature and the number of cups of hot chocolate sold.