daphne6793
Answered

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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
Use 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.

Sagot :

brownclive90
Answer:
55.44 inches
Step-By-Step Explanation
part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.
slope = m = (change in rainfall)/(change in years)
= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53
then the point-slope form of the equation of the line can be written as
y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)
y = -0.53x +62.33 . . . x = years after 2004
part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is
y = -0.53·13 +62.33 = 55.44 . . inches
the predicted rainfall in 2017 is 55.44 inches.
MrRoyal

The linear equation that represents the table is [tex]y = -0.53x + 62.33[/tex]

What are linear functions?

A linear function is a graph that has a constant rate.

From the table, we have the following ordered pairs

(x,y) = (0,62.33) and (1, 61.8)

Start by calculating the slope (m)

[tex]m = \frac{y_2 -y_1}{x_2-x_1}[/tex]

So, we have:

[tex]m = \frac{61.8 -62.33}{1-0}[/tex]

[tex]m = -0.53[/tex]

The linear equation is then calculated as:

[tex]y = m(x -x_1) + y_1[/tex]

So, we have:

[tex]y = -0.53(x -0) + 62.33[/tex]

Expand

[tex]y = -0.53x + 62.33[/tex]

Hence, the linear equation that represents the table is [tex]y = -0.53x + 62.33[/tex]

Read more about linear equations at:

https://brainly.com/question/14323743

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