a. An approximate equation of the line of best fit is: y = 0.5x - 20.
b. The predicted monthly heating cost for a month with an average temperature of 25 °F is -$17.50.
(a) Write an approximate equation of the line of best fit for the data.
To approximate the equation of the line of best fit, we can use the following steps:
Draw a line that visually appears to fit the data points well.
Estimate the slope and y-intercept of the line.
Write the equation of the line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
From the graph, it appears that the line of best fit has a positive slope and a negative y-intercept. The slope of the line is approximately 0.5, and the y-intercept of the line is approximately -20.
Therefore, an approximate equation of the line of best fit is:
y = 0.5x - 20
(b) Using your equation from part (a), predict the monthly heating cost for a month with an average temperature of 25 °F.
To predict the monthly heating cost for a month with an average temperature of 25 °F, we can simply plug x = 25 into the equation of the line of best fit:
y = 0.5(25) - 20 = 2.5 - 20 = -17.5
Therefore, the predicted monthly heating cost for a month with an average temperature of 25 °F is -$17.50.