For the past ten years, Michelle has been tracking the average annual rainfall in Boynton Beach, Florida by recording her data in the given table. She has concluded that the relationship can be modeled by a linear function.
Year 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Average Rainfall(in inches) 62.33 61.8 61.27 60.74 60.21 59.68 59.15 58.62 58.09 57.56Use the values provided in the table to create a linear graph of the data. On the graph, let x=0
represent the year 2004. Be sure to include all proper labels on the graph.
We can create a linear graph by plotting the average rainfall as the y-coordinate and the year as the x-coordinate. To let x=0 represent the year 2004, we can subtract 2004 from each year. This gives us the following data to plot:
Year 0 1 2 3 4 5 6 7 8 9
Average Rainfall (in inches) 62.33 61.8 61.27 60.74 60.21 59.68 59.15 58.62 58.09 57.56
We can now plot these points on a graph with the x-axis representing the years and the y-axis representing the average rainfall.
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0 2 4 6 8
2004 2006 2008 2010 2012
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We can see that the points form a roughly straight line, which confirms Michelle's conclusion that the relationship can be modeled by a linear function. We can also use the points to find the equation of the line using linear regression or the slope-intercept form:
y = mx + b where m is the slope and b is the y-intercept.
Using linear regression, we can get the following equation to model the data:
y = -0.307x + 62.33 where x represents the year (starting at 0 for 2004) and y represents the average rainfall.
Alternatively, we can find the slope and y-intercept by selecting two points from the graph, such as (0, 62.33) and (9, 57.56), and using the formula:
m = (y2 - y1)/(x2 - x1) and b = y1 - mx1
m = (57.56 - 62.33)/(9 - 0) = -0.307 and b = 62.33
Therefore, the equation of the line is y = -0.307x + 62.33.
Either way, we can use this equation to predict the average rainfall for future years or to estimate the average rainfall for years before 2004.