Q9. - 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. Theater   Broadway, in New York City, is the center of American theater. The table shows the total revenue of all Broadway play for some recent seasons.

Season	95-96	96-97	97-98	98-99	99-00	09-10
Revenue($ millions	436	499	558	588	603	?

Step-by-Step Solution

Answer

a.

b. A predicted equation is $y=44.5x-454.5$

c. The model predicted that the total revenue of all Broadway plays will be about $1078 million or about $$1.1$ billion in 2009-2010 season $1.1$

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 a line of fit is often called a prediction equation.

Step-2 – Determine the axis.

For exercise 9, we take Season at the x-axis and revenue at the y-axis, we get

$(95-96,436),(96-97,499),(97-98,558),(98-99,588) and (99-00,603)$

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 $(1,499) and (3,588)$

  $\begin{array}{l}Slope=\frac{588-499}{3-1}[\because \text{ Slope =}\frac{y_2-y_1}{x_2-x_1}]\\ =\frac{89}{2}\\ =44.5\end{array}$

Step-3 – Determine the equation.

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

Substituting values

 $\begin{array}{l}(y-499)=44.5(x-1)\\ y-499=44.5x-44.5\\ y=44.5x-454.5\end{array}$

Hence, a predicted equation is $y=44.5x+454.5$

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 Revenue value for seasons 09-10 is missing, so we substitute $x=14$ in the predicted equation to get the value of x.

Step-3 – Calculation

 $\begin{array}{l}y=44.5x+454.5\\ y=44.5\left(14\right)+454.5\\ y=1078\end{array}$

 Hence, the missing value is $x=1078$.