Answer:
• (a)y = 1425 - 19.87x
,
• (b)The model predicts that the amount of gas consumed in a month when the temperature is 42 degrees Fahrenheit is 590.46 cubic ft.
,
• (c)For every degree increase in the temperature, the amount of gas consumed reduces by 19.87 cubic feet.
,
• (d)When the temperature is 0 degrees, the amount of gas consumed is 1425 cubic feet.
Explanation:
The relationship between the average temperature in a given month and the amount of gas needed to heat a particular home is:
[tex]\begin{gathered} \hat{y}=a+bx \\ y=\text{amount of gas} \\ x=\text{temperature} \end{gathered}[/tex]
Part A
• The slope of the line, b = -19.87
,
• The y-intercept, a = 1425.
The equation of the line of best fit is:
[tex]\hat{y}=1425-19.87x[/tex]
Part B
When the average temperature, x = 42 degrees.
[tex]y=1425-19.87(42)=1425-834.54=590.46[/tex]
The model predicts that the amount of gas consumed in a month when the temperature is 42 degrees Fahrenheit is 590.46 cubic ft.
Part C
The slope of the line = -19.87
This means that for every degree increase in the temperature, the amount of gas consumed reduces by 19.87 cubic feet.
Part D
By definition, the y-intercept is the value of y at which x is 0.
When x=0
[tex]y=1425-19.87(0)=1425\text{ cubic ft.}[/tex]
A y-intercept of 1425 cubic feet mean that when the temperature is 0 degrees, the amount of gas consumed is 1425 cubic feet.
