Question

How do you use the prediction equation to predict the missing value?
The prediction equation is \[y=1.67x-3269.64\].
Explain how the answer to the missing value is about 87 million.
As more channels have been added, cable television has become attracted to more viewers. The table shows the number of U.S. households with cable service in some recent years.

Year	1990	1992	1994	1996	1998	2010
Households(millions)	55	57	59	65	67	?

Answer 1

Hint: In this problem, we have to find the missing value using the prediction equation. We know that the given equation is \[y=1.67x-3269.64\]. We can substitute the year 2010 in the missing data in the equation and can find the missing value. We can assume x for the year and assume y for the households.

Complete step by step answer:
We know that the given prediction equation is,
\[y=1.67x-3269.64\]
We can assume that, x as the year and y as the households.
We can draw the table here.

Year(x)	1990	1992	1994	1996	1998	2010
Households(y)(millions)	55	57	59	65	67	?

Now we can substitute the year, which is above the missing value in the given prediction equation, i.e., x = 2010.
\[\begin{align}
  & \Rightarrow y=1.67\left( 2010 \right)-3269.64 \\
 & \Rightarrow y=87.06 \\
\end{align}\]

Therefore, the number of households is approximately 87 million.

Note: Students make mistakes while substituting the correct value and simplifying the substituted value, which should be concentrated. We may get confused after seeing the question, but we have to go through the question properly and understand what id being asked to solve these types of problems.