Question

carlos 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.
the rate of change in the days high temperature for every additional hot cocoa sold.
the average change in the number of hot cocoas sold for every additional degree of the days high temperature.
a prediction of number of hot cocoas sold when the temperature is 1°f.

Explanation:

Step1: Recall the concept of slope in a linear relationship

In a linear relationship \(y = mx + b\) (where \(y\) is the dependent variable, \(x\) is the independent variable, \(m\) is the slope and \(b\) is the y - intercept), the slope \(m=\frac{\Delta y}{\Delta x}\). In the context of the problem, the dependent variable \(y\) is the number of hot - cocoas sold and the independent variable \(x\) is the high temperature.

Step2: Interpret the slope formula in terms of the problem

The formula for slope \(m = \frac{\text{Change in }y}{\text{Change in }x}\). Here, a change in \(y\) represents a change in the number of hot - cocoas sold and a change in \(x\) represents a change in temperature. So, the slope represents the average change in the number of hot - cocoas sold (\(\Delta y\)) for a unit change in temperature (\(\Delta x = 1\) degree Fahrenheit).

Answer:

The average change in the number of hot cocoas sold for every additional degree of the day’s high temperature.