Question

Data about the outside temperature and gas used for heating a building are given in the table.

Use a graphing calculator to create the line of best fit for the data.
temperature
(deg F) gas usage
(therms)
58 5,686
62 7,373
64 5,805
67 5,636
70 3,782
73 3,976
74 3,351
74 3,396
75 2,936
73 3,078
65 4,549
59 7,022
58 6,106
62 4,566
64 4,608
67 5,790
70 6,501
73 3,843
What is the equation of the line of best fit for this data? Round numbers to the nearest whole number.
What is the slope of the line of best fit? What does it mean in this situation?
What does the line of best fit estimate for gas usage when the outside temperature is 59 degrees Fahrenheit?
How does the actual gas usage compare to the estimated gas usage when the outside temperature is 59 degrees Fahrenheit?

Answer 1

The equation of the line of best fit for this data is y = -106x + 6178.

The slope of the line of best fit is -106. This means that for every degree increase in temperature, the gas usage decreases by 106 therms.

The line of best fit estimates that when the outside temperature is 59 degrees Fahrenheit, the gas usage will be 7,022 therms.

The actual gas usage when the outside temperature is 59 degrees Fahrenheit is 6,106 therms. This means that the estimated gas usage is slightly higher than the actual gas usage.

Answer 2

Step-by-step explanation:

A) y = -180x + 16938

B) The slope is -180. This means that for every increase in temperature/degrees the gas usage will decrease by 180.

C) -180x + 16938 = 6318 When the temperature is 59 degrees Fahrenheit the line of best fit estimates 6318 gas usage.

D) The gas usage when the temperature is 59 degrees is 7022 on the table, but the gas usage estimated is 6318. The difference is 704

-Hope this helps.