Question

The scatter plot shows the average monthly temperature, x, and the monthly heating cost of a family, y, for 23 different months.Use the equation of the line of best fit, =y+−1.24x96.40, to answer the questions below.Give exact answers, not rounded approximations. (a) What is the predicted heating cost for a month with an average temperature of 0°F?$(b) What is the predicted heating cost for a month with an average temperature of 25°F?$(c) For an increase of one degree Fahrenheit, what is the predicted decrease in the monthly heating cost?$

Answer 1

From the information given,

The equation of the best line of fit is

y = - 1.24x + 96.4

where

x represents the temperature in degrees fahrenheit

y represents the monthly heating temperature

A

To find the predicted heating cost at 0 degree fahrenheit, we would substitute x = 0 into the equationwe have

y = - 1.24(0) + 96.4

y = 96.4

Predicted heating cost = $96.4

B

We would substitute x = 25 into the equation. We have

y = - 1.24(25) + 96.4 = 65.4

Predicted heating cost = 65.4

C

We would determine the slope of the equation. Recall, the equation of a line in the slope intercept form is expressed as

y = mx + c

where

m is the slope

c is the y intercept

By comparing the equation of the best line of fit with the slope intercept equation,

slope, m = - 1.24

Predicted decrease = $ - 1.24