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 represent the year 2004. Be sure to include all proper labels on the graph.

Answer:

The answer is below

Step-by-step explanation:

A linear function is a function in the form y = mx + b, where y and x are variables, b is the y intercept (value of y at x = 0) and m is the slope (rate of change).

Let x represent the year and y represent the amount of rainfall in inches. The linear function can be gotten by selecting any two pair of points from the table in the form (x, y).

Let us use the points (2004, 62.33) and (2007, 60.74). The equation is gotten using:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-62.33=\frac{60.74-62.33}{2007-2004}(x-2004) \\\\y-62.33=-0.53(x-2004)\\\\y-62.33=-0.53x+1062.12\\\\y=-0.53x+1124.45[/tex]

The graph is plotted using geogebra.

The average rainfall from 2004 to 2013 is 59.945

Given data of rainfall:

2004    62.33

2005    61.8

2006    61.27

2007    60.74

2008    60.21

2009    59.68

2010    59.15

2011     58.62

2012    58.09

2013    57.56

it is the sum of all the observations divided by the total number of observations.

average rainfall A

(62.33+61.8+61.27+60.74+60.21+59.68+59.15+58.62+58.09+57.56)/10

A= 59.945

thus, the average rainfall from 2004 to 2013 is 59.945

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