Question

for questions 6 through 10, the scatter plot shows the relationship between the average monthly temperature, in degrees fahrenheit (°f), and the monthly sales of heaters. the equation ( y = - 1.4 x + 129.18 ) can be used to model the relationship between the temperature, ( x ), and heater sales, ( y ). 6. find the slope of the model. 7. determine the ( y )-intercept of the model. 8. what does the slope represent in the context? 9. determine an appropriate domain in the context. 10. determine an appropriate range in the context.

Explanation:

Step1: Identify the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

Step2: Find the slope for question 6

Given \(y=-1.4x + 129.18\), comparing with \(y = mx + b\), the slope \(m=-1.4\).

Step3: Find the \(y\) - intercept for question 7

Given \(y=-1.4x + 129.18\), comparing with \(y = mx + b\), the \(y\) - intercept \(b = 129.18\).

Step4: Interpret the slope for question 8

The slope \(m=-1.4\). In the context of temperature (\(x\)) and heater sales (\(y\)), for every 1 - degree Fahrenheit increase in temperature, the number of heater sales decreases by \(1.4\).

Step5: Determine the domain for question 9

Looking at the scatter - plot, the \(x\) - values (temperature) range from approximately \(20^{\circ}F\) to \(80^{\circ}F\). So the domain is \(20\leq x\leq80\).

Step6: Determine the range for question 10

Looking at the scatter - plot, the \(y\) - values (heater sales) range from approximately \(30\) to \(110\). So the range is \(30\leq y\leq110\).

Answer:

1. The slope is \(-1.4\).
2. The \(y\) - intercept is \(129.18\).
3. For every 1 - degree Fahrenheit increase in temperature, the number of heater sales decreases by \(1.4\).
4. The domain is \(20\leq x\leq80\).
5. The range is \(30\leq y\leq110\).