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 57.56
To model this relationship as a linear function, the first thing we need to do is find the slope or rate of change of the average rainfall. We do this by selecting two points on the table and calculating:
Slope (m) = (Change in Rainfall) / (Change in Year)
Using the data for 2004 and 2013, we get:
m = (57.56 - 62.33) / (2013 - 2004)
m = (-4.77) / 9
m = -0.53
Now that we have the slope, we can find the equation of the line in the form y = mx + b, where y represents average rainfall, x represents the year, and b is the y-intercept (the value of y when x=0). To find b, we can use the year 2004 and the average rainfall for 2004:
62.33 = -0.53(2004) + b
b = 62.33 + 1062.12
b = 1124.45
So, the linear function that models the relationship between year and average annual rainfall in Boynton Beach, Florida is:
y = -0.53x + 1124.45
Now we can use this equation to predict average rainfall in any given year by substituting the year for x.