Question

The following scatter plot shows the relationship between the average temperature in a givenmonth and the amount of gas needed to heat a particular home.The slope of the line is -19.87and the y-intercept is 1425.Answer all parts on picture pls.

Answer 1

• (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:

`\begin{gathered} \hat{y}=a+bx \\ y=\text{amount of gas} \\ x=\text{temperature} \end{gathered}`

Part A

• The slope of the line, b = -19.87

,

• The y-intercept, a = 1425.

The equation of the line of best fit is:

`\hat{y}=1425-19.87x`

Part B

When the average temperature, x = 42 degrees.

`y=1425-19.87(42)=1425-834.54=590.46`

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

`y=1425-19.87(0)=1425\text{ cubic ft.}`

A y-intercept of 1425 cubic feet mean that when the temperature is 0 degrees, the amount of gas consumed is 1425 cubic feet.