Question content area top left
Part 1
The graph shows the number of wireless subscriber connections (that is, active devices, including smartphones, feature phones, tablets, etc.) in millions in a country for the years 2011 through 2016. Complete parts (a) through (c) below.
Question content area bottom left
Part 1
(a) In the context of this graph, what does the ordered pair (2016, 179) mean?
In 20162016, there were 179179 million wireless subscriber connections in the United States.
Part 2
(b) Use the given ordered pairs to find the slope of the line.
The slope of the line is 1414.
(Simplify your answer.)
Part 3
(c) Interpret the slope in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The number of subscribers decreased by an average of enter your response here million per year from 2011 through 2016. (Simplify your answer.)
B.
The number of subscribers increased by an average of enter your response here million per year from 2011 through 2016. (Simplify your answer.)
C.
The number of subscribers did not change from 2011 through 2016.
.
.
.
Question content area right
Part 1
Wireless Subscriber Connections
2011
2012
2013
2014
2015
2016
0
40
80
120
160
200
Year
Subscriber Connections (in millions)
(2011,109)
(2016,179)
y
x
A coordinate plane labeled "Wireless Subscriber Connections" has a horizontal x-axis labeled "Year" from 2011 to 2016 in increments of 1 and a vertical y-axis labeled "Subscriber Connections in millions" from 0 to 200 in increments of 40. A plotted line segment has labeled endpoints at (2011, 109) and (2016, 179).
(a) In the context of this graph, the ordered pair (2016, 179) means that in 2016, there were 179 million wireless subscriber connections in the country.
(b) To find the slope of the line, we need to calculate the change in y divided by the change in x.
Change in y = 179 - 109 = 70
Change in x = 2016 - 2011 = 5
Slope = Change in y / Change in x = 70 / 5 = 14
(c) The slope of 14 means that the number of subscribers increased by an average of 14 million per year from 2011 through 2016.
(a) In the context of this graph, the ordered pair (2016, 179) means that in the year 2016, there were 179 million wireless subscriber connections in the country.
(b) To find the slope of the line, we can use the formula:
Slope = (change in y) / (change in x)
Given the ordered pairs (2011, 109) and (2016, 179), the change in y = 179 - 109 = 70, and the change in x = 2016 - 2011 = 5.
So, the slope of the line is:
Slope = (change in y) / (change in x) = 70 / 5 = 14
(c) The slope of 14 means that the number of subscribers increased by an average of 14 million per year from 2011 through 2016.
To answer part (a), we need to understand what the ordered pair (2016, 179) means in the context of the graph. In this case, the x-coordinate represents the year 2016, and the y-coordinate represents the number of wireless subscriber connections, which is 179 million. Therefore, the ordered pair (2016, 179) means that in the year 2016, there were 179 million wireless subscriber connections in the country.
To answer part (b), we need to find the slope of the line using the given ordered pairs. The slope of a line can be determined using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Using the ordered pairs (2011, 109) and (2016, 179), we can calculate the change in y-coordinates and the change in x-coordinates:
Change in y-coordinates = 179 - 109 = 70
Change in x-coordinates = 2016 - 2011 = 5
Plugging these values into the slope formula, we get:
slope = 70 / 5 = 14/1 = 14
Therefore, the slope of the line is 14.
Now, to answer part (c), we need to interpret the slope in the context of the problem. Since the slope represents the average rate of change between two points on the line, it tells us how the number of subscribers changed on average per year from 2011 to 2016.
A positive slope indicates an increase, while a negative slope indicates a decrease. In this case, since the slope is positive (14), we can conclude that the number of subscribers increased on average by 14 million per year from 2011 through 2016. Therefore, the correct interpretation is choice B:
The number of subscribers increased by an average of 14 million per year from 2011 through 2016.