Question

the line graph shows the average fuel economy (in miles per gallon) of passenger automobiles produced during each of the model years shown. of the following line segments, which has the greatest slope: from 2008 to 2009, 2011 to 2012, or 2016 to 2017? the line segment from has the greatest slope of (type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Calculate slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line segment. For the years, \(x\) - axis represents the year and \(y\) - axis represents the average miles per gallon.

Step2: Slope from 2008 to 2009

Let \(x_1 = 2008,y_1\approx27\) (approximate value from the graph), \(x_2=2009,y_2\approx26\). Then \(m_1=\frac{26 - 27}{2009 - 2008}=\frac{- 1}{1}=-1\)

Step3: Slope from 2011 to 2012

Let \(x_1 = 2011,y_1\approx24\) (approximate value from the graph), \(x_2=2012,y_2\approx23\). Then \(m_2=\frac{23 - 24}{2012 - 2011}=\frac{-1}{1}=-1\)

Step4: Slope from 2016 to 2017

Let \(x_1 = 2016,y_1\approx21\) (approximate value from the graph), \(x_2=2017,y_2\approx19\). Then \(m_3=\frac{19 - 21}{2017 - 2016}=\frac{-2}{1}=-2\)

Since \(\vert m_3\vert>\vert m_1\vert=\vert m_2\vert\)

Answer:

The line segment from 2016 to 2017 has the greatest slope.