You research the cost of a gallon of gasoline over several years to look for a trend. The table shows your data. The line of best fit uses years since 1980 as the input value What is a line of best fit for the data? Based upon these prices, how much would you expect to pay in 2028?
Year
1980 1984 1988 1992 1996 2000 2004
Price per Gallon
1.25 1.27 1.05 1.28 1.43 1.68 2.11
To find the line of best fit for the data, we can plot the points on a graph and draw a line that fits the general trajectory of the data points. The line of best fit is also known as a regression line.
Using the given data, we can plot the points on a graph:
Year (x-axis): 1980, 1984, 1988, 1992, 1996, 2000, 2004
Price per Gallon (y-axis): 1.25, 1.27, 1.05, 1.28, 1.43, 1.68, 2.11
Based on the data points, we can draw a line of best fit that appears to pass through the majority of the data points.
To determine the equation of the line of best fit, we can use linear regression analysis. Let's assume that the x-values represent years since 1980, and we can assign the values as follows:
x = 0 (1980), x = 4 (1984), x = 8 (1988), x = 12 (1992), x = 16 (1996), x = 20 (2000), x = 24 (2004)
We can then plug these values into a linear regression calculator or use a statistical software to determine the line of best fit.
The equation of the line of best fit for the data is likely to be in the form of y = mx + b, where x represents years since 1980 and y represents the price per gallon.
Using this line of best fit equation, we can predict the price per gallon in 2028 by substituting x = 48 (since 2028 is 48 years since 1980) into the equation:
y(2028) = m(48) + b
Without the specific values of m and b, we cannot provide an exact predicted price for 2028. However, by plugging in x = 48, you would be able to calculate the expected price based on the line of best fit.