Question

brody has a part - time job at an ice skating rink selling hot cocoa. he decided to plot the number of hot cocoas he sold relative to the days high temperature and then draw the line of best fit. what does the slope of the line represent?
answer
a prediction of the temperature when 1 hot cocoa is sold.
a prediction of number of hot cocoas sold when the temperature is 1°f.
the rate of change in the expected number of hot cocoas over the days high temperature.
the rate of change in the days high temperature for every additional hot cocoa sold.

Explanation:

Step1: Recall the concept of slope in a linear regression line

In a scatter - plot with a line of best fit (linear regression line) \(y = mx + b\) (where \(y\) is the dependent variable, \(x\) is the independent variable, \(m\) is the slope and \(b\) is the y - intercept), the slope \(m=\frac{\Delta y}{\Delta x}\).

Step2: Interpret the variables in the context of the problem

Here, the \(x\) - axis represents the number of hot - cocoas sold and the \(y\) - axis represents the high temperature. The slope \(m=\frac{\text{Change in }y}{\text{Change in }x}\). In terms of the problem, \(y\) is the high temperature and \(x\) is the number of hot - cocoas sold. So, \(m=\frac{\text{Change in high temperature}}{\text{Change in number of hot - cocoas sold}}\)

Answer:

The rate of change in the day's high temperature for every additional hot cocoa sold.