Question

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: Recall the 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. Assume \(x\) represents the year and \(y\) represents the miles - per - gallon value.

Step2: Calculate the slope for 2008 - 2009

Let \((x_1,y_1)=(2008,28)\) and \((x_2,y_2)=(2009,26)\). Then \(m_{2008 - 2009}=\frac{26 - 28}{2009 - 2008}=\frac{-2}{1}=-2\).

Step3: Calculate the slope for 2011 - 2012

Let \((x_1,y_1)=(2011,24)\) and \((x_2,y_2)=(2012,23)\). Then \(m_{2011 - 2012}=\frac{23 - 24}{2012 - 2011}=\frac{-1}{1}=-1\).

Step4: Calculate the slope for 2012 - 2016

Let \((x_1,y_1)=(2012,23)\) and \((x_2,y_2)=(2016,19)\). Then \(m_{2012 - 2016}=\frac{19 - 23}{2016 - 2012}=\frac{-4}{4}=-1\).

Step5: Calculate the slope for 2016 - 2017

Let \((x_1,y_1)=(2016,19)\) and \((x_2,y_2)=(2017,18)\). Then \(m_{2016 - 2017}=\frac{18 - 19}{2017 - 2016}=\frac{-1}{1}=-1\).

Answer:

From 2008 to 2009.