Q5. - Algebra 2

Question

Complete parts a–c for each set of data in Exercises 4 and 5.

a. Draw a scatter plot.

b. Use two ordered pairs to write a prediction equation.

c. Use your prediction equation to predict the missing value.

5. TELEVISION As more channels have been added, cable television has become attractive to more viewers. The table shows the number of U.S. households with cable service in some recent year.

Step-by-Step Solution

Answer

a. 

b. a predicted equation is $y=1.67x-3269.64$

c. About 87 million households will have cable service in 2010.

(a) Step-1 – Concept of scatter plot

A scatter plot is a kind of plot where we use Cartesian coordinates to display values for typically two variables for a set of data.

Step-2 – Write given information

The table shows the number of U.S. households with cable service in some recent year.

Step-3 – Constructing scatter plot

We take “year” at the x axis and “Households” at the y-axis, we get

(b) Step-1 – Concept of Predicted equation

An predicted equation of a line can be used to predict one of the variables given the other variable.

Step-2 – Calculate slope

Using points (1992,57) and (1998,67)

Slope = $\frac{67-57}{1998-1992}$   $[\because \text{ Slope =}\frac{y_2-y_1}{x_2-x_1}]$

$\begin{array}{l}=\frac{10}{6}\\ =1.67\text{\hspace{0.17em}(approx)}\end{array}$

Step-3 – Using point-slope form

Point slope form : $(y-y_1)=m(x-x_1)$

Substituting values

$\begin{array}{l}(y-57)=1.67(x-1992)\\ y=1.67x-3269.64\end{array}$

Hence, a predicted equation is $y=1.67x-3269.64$

(c) Step-1 – Use of Predicted equation

An predicted equation of a line can be used to predict one of the variables given the other variable.

Step-2 – Missing value

The households value for year 2010 ft is missing, so we substitute x= 2010 in the predicted equation to get the value of y.

Step-3 – Calculation

Equation becomes,

 $\begin{array}{l}y=1.67\left(2010\right)-3269.64\\ =87\text{ (approx)}\end{array}$

Hence, About 87 million households will have cable service in 2010.