Question

find the slope of the line and write a sentence explaining the meaning of the slope as a rate of change. attach the proper units. this graph approximates the number of households that have an internet subscription y (in millions) for year x. the slope of the line is m = (type an integer or a decimal.) select the correct choice below and fill in the answer box within your choice. (type an integer or a decimal.) a. every 2 years, there are million(s) less households with an internet subscription. b. every year, there are million(s) less households with an internet subscription. c. every year, there are million(s) more households with an internet subscription. d. every 2 years, there are million(s) more households with an internet subscription.

Explanation:

Step1: Recall the formula for slope

The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x\) represents the year and \(y\) represents the number of households (in millions).

Step2: Identify two points from the graph

We can take the points \((2014,118)\) and \((2019,124)\).

Step3: Calculate the change in \(y\) and \(x\)

\(\Delta y=y_2 - y_1=124 - 118 = 6\), \(\Delta x=x_2 - x_1=2019 - 2014=5\). But wait, no, the slope is given as \(m = 1.2\). The meaning of slope in the context of a linear equation \(y=mx + b\) (where \(y\) is the number of households in millions and \(x\) is the year) is the rate of change.

Since \(m=\frac{\Delta y}{\Delta x}\), and \(m = 1.2\). This means that for each unit increase in \(x\) (each year), \(\Delta y=1.2\).

Answer:

C. Every year, there are \(1.2\) million(s) more households with an Internet subscription.