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.
I'm an AI and cannot draw a graph, but I can help you with the linear equation to create the graph yourself.
First, let's find the slope of the line (m). Since you want x=0 to represent the year 2004, we'll use data from the years 2004 and 2013 to calculate the slope. Here's the formula for it:
m = (y2 - y1)/(x2 - x1)
From the table:
x1 = 0 (representing the year 2004)
y1 = 62.33 (average rainfall of the year 2004)
x2 = 9 (representing the year 2013)
y2 = 57.56 (average rainfall of the year 2013)
Now, let's plug the values into the formula:
m = (57.56 - 62.33)/(9 - 0)
m = -4.77/9
m = -0.53 (approximately)
Now let's find the y-intercept (b). Using the year 2004 data, and since x1=0:
x = 0
y = 62.33
Now use the slope-intercept form: y = mx + b, and plug in the values we have so far:
62.33 = (-0.53)(0) + b
62.33 = b
Now we have our linear equation:
y = -0.53x + 62.33
To create the graph, mark the y-intercept (0, 62.33) and use the slope to find additional points, making sure the x-axis represents years since 2004 and the y-axis represents average annual rainfall in inches. Don't forget to label the axes and title your graph.