Question

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: 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.

Step2: Calculate the slope for each interval

• For 2008 - 2009:

Let \(x_1 = 2008\), \(y_1\approx31.5\); \(x_2 = 2009\), \(y_2\approx30\).
\(m_1=\frac{30 - 31.5}{2009 - 2008}=\frac{- 1.5}{1}=-1.5\)

• For 2011 - 2012:

Let \(x_1 = 2011\), \(y_1\approx33\); \(x_2 = 2012\), \(y_2\approx34\).
\(m_2=\frac{34 - 33}{2012 - 2011}=\frac{1}{1}=1\)

• For 2016 - 2017:

Let \(x_1 = 2016\), \(y_1\approx37\); \(x_2 = 2017\), \(y_2\approx35\).
\(m_3=\frac{35 - 37}{2017 - 2016}=\frac{-2}{1}=-2\)

Answer:

2016 - 2017