SOLUTION: 3. The linear equation y=0.16x + 1.22 represents an estimate of the average cost of gas for year x starting in 2003. The year 2004 would be represented by x = 1, for example, as it
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Question 455374: 3. The linear equation y=0.16x + 1.22 represents an estimate of the average cost of gas for year x starting in 2003. The year 2004 would be represented by x = 1, for example, as it is the first year in the study. Similarly, 2009 would be year 6, or x = 6.
1. What year would be represented by x=9?
2. What x-value represents the year 2020?
3. What is the slope (or rate of change) of this equation?
4. What is the y-intercept?
5. What does the y-intercept represent?
6. Assuming this growth trned continues, what will the price of gasoline be in the year 2020? How did you arrive at your answer?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
y = 0.16x + 1.22
.
| x-value | Year
|
| 0 | 2003
|
| 1 | 2004
|
| 2 | 2005
|
| 3 | 2006
|
| 4 | 2007
|
| 5 | 2008
|
| 6 | 2009
|
| 7 | 2010
|
| 8 | 2011
|
| 9 | 2012
|
| 10 | 2013
|
| 11 | 2014
|
| 12 | 2015
|
| 13 | 2016
|
| 14 | 2017
|
| 15 | 2018
|
| 16 | 2019
|
| 17 | 2020
|
.
The given equation is in slope-intercept form, so you can answer a couple of questions by inspection.
y = 0.16x + 1.22
slope = 0.16
y-intercept = 1.22
That means the price of gas was $1.22 in 2003.
.
x-intercept is where y=0, so we solve
0 = 0.16x + 1.22
-.16x = 1.22
x = 1.22/-.16
x = -7.625
.
What does this linear model forecast the price of gas in 2020 to be?
x=17
y = 0.16*17 + 1.22
y = 2.72 + 1.22
y = 3.94
.
Done
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