Question

the figure shows the net profits (in billions of dollars) for wal - mart from 2012 through 2016.
wal - mart
(a) find the slope (in billions of dollars per year) of each line segment. (enter your answers as a comma - separated list. the order of your answers should match the order in which the line segments occur on the graph from left to right.)
17.0, 16.7, 16.4, 14.7, 13.5
(b) find the slope (in billions of dollars per year) of the line segment connecting the years 2012 and 2016.
enter a number.
interpret the meaning of the slope in the context of the problem.
the slope represents the average annual change in the net profit over the given interval.
the slope represents the total change in the net profit in year 2016.
the slope represents the total change in the net profit in year 2012.
the slope represents the total change in the net profit over the given interval.
the slope represents the average monthly change in the net profit over the given interval.

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Find slopes for part (a)

For the line - segment from $(2012,17.0)$ to $(2013,16.7)$:
$m_1=\frac{16.7 - 17.0}{2013 - 2012}=\frac{- 0.3}{1}=-0.3$
For the line - segment from $(2013,16.7)$ to $(2014,16.4)$:
$m_2=\frac{16.4 - 16.7}{2014 - 2013}=\frac{-0.3}{1}=-0.3$
For the line - segment from $(2014,16.4)$ to $(2015,14.7)$:
$m_3=\frac{14.7 - 16.4}{2015 - 2014}=\frac{-1.7}{1}=-1.7$
For the line - segment from $(2015,14.7)$ to $(2016,13.5)$:
$m_4=\frac{13.5 - 14.7}{2016 - 2015}=\frac{-1.2}{1}=-1.2$
The slopes for part (a) are $-0.3,-0.3,-1.7,-1.2$.

Step3: Find slope for part (b)

For the line - segment connecting $(2012,17.0)$ and $(2016,13.5)$:
$m=\frac{13.5 - 17.0}{2016 - 2012}=\frac{-3.5}{4}=-0.875$
The slope represents the average annual change in the net profit over the given interval.

Answer:

(a) $-0.3,-0.3,-1.7,-1.2$
(b) $-0.875$; The slope represents the average annual change in the net profit over the given interval.