(Need answers ASAP!) The scatter plot shows the relationship between the average temperature (in degrees Fahrenheit) and a person's monthly heating bill (in dollars). The equation that represents the graph is: y = -2.2x + 210.

1. The slope of the linear model is -2.2. What does that mean in terms of the monthly heating bill and average temperature?

2. The national weather service estimates that the average temperature for next month will be 55 degrees. Estimate the monthly heating bill for this month. Is this estimate reasonable? Explain your reasoning.

3. What is the y-intercept of the linear model given? What does it mean in the context of the problem? Is this reasonable? Explain your reasoning

Please see detailed explanation below.

Step-by-step explanation:

1.  The slope of the best-fit line tells us how the dependent variable (y) changes for every 1 unit increase in the independent (x) variable, on average.

The slope of a line is a value that describes the rate of change between the independent and dependent variables. The slope tells us how the dependent variable (y) changes for every 1-unit increase (or decrease) in the independent (x) variable, on average.

In the given problem, what the slope represents is that the monthly heating bill decreases by 2.2 for every increase in average temperature. This makes sense because as the temperature rises, the monthly cost for the heating bill should decrease because you don't need as much heating when the average temperatures are higher.  

2. The national weather service estimates that the average temperature for next month will be 55 degrees. Estimate the monthly heating bill for this month. Is this estimate reasonable? Explain your reasoning.

Since the national weather service estimates that the average temperature for next month will be 55°F, then we can plug this value in the given equation:

y = -2.2x + 210  

y = -2.2(55°) + 210

y = -121 + 210

y = 89

Therefore, the predicted heating bill for next month will be $89.  

The estimate seems reasonable because 55°F is within the domain of the observed x values in the data. Also, in looking at the plotted points on the scatter plot. there is a point where it is close to what we solved here in question #2 (55°F, $89).  

3. What is the y-intercept of the linear model given? What does it mean in the context of the problem? Is this reasonable? Explain your reasoning

The y -intercept is the point where the graph crosses the y -axis (it is the value of y when x = 0). The y-intercept of the given model is 210. This represents the flat heating fee or cost for a month when the average temperature is 0°F. In the context of the given problem, I think that a y-intercept value of 210 is quite reasonable because households use more heating in colder temperatures, let alone when the average temperature is 0°F.  

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of