Q8. - Algebra 2

Question

Complete parts a-c for each set of data in Exercises 6-9

1. Draw a scatter plot
2. Use two ordered pair to write a prediction equation.
3. Use your prediction equation to predict the missing value. 

6. Health   Bottled water has become very popular. The table shows the number of gallons of bottled water consumed per person in some recent years.

Step-by-Step Solution

Answer

a.

b. A predicted equation is $y=1.03x-2043.39$

c. The model predicts that about $26.9$ gallons of the bottled water will be consumed per person in 2010. 

a. Step-1 – Concept of scatter plot

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

Prediction equation – An equation of line of fit is often called a prediction equation.

Step-2 – Determine the axis.

For exercise 8, we take Years at the x axis and Gallons at the y-axis, we get

$(1992,8.2),(1993,9.4),(1994,10.7)(1995,11.6) ,(1996,12.5)and (1997,13.1)$

Step-3–Constructing scatter plot.

b. Step-1 – Concept of Predicted equation

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

Step-2 – Calculate slope

Using points$(1993,9.4) and (1996,12.5)$

  $\begin{array}{l}Slope=\frac{18.2-16.5}{1998-1996}[\because \text{ Slope =}\frac{y_2-y_1}{x_2-x_1}]\\ =\frac{3.1}{3}\\ =1.03\end{array}$

Step-3 – Determine the equation.

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

Substituting values

 $\begin{array}{l}(y-9.4)=1.03(x-1993)\\ y-9.4=1.03x-2052.79\\ y=1.03x-2043.39\end{array}$

Hence, a predicted equation is $y=1.03x-2043.39$

c. Step-1 – Use of Predicted equation

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

Step-2 – Missing value

The Gallons value for years 2010 is missing, so we substitute $x=2010$ in the predicted equation to get the value of y.

Step-3 – Calculation

 $\begin{array}{l}y=1.03x-2043.39\\ y=1.03\left(2010\right)-2043.39\\ y=26.9\end{array}$

 Hence, the missing value is $y=26.9$