Q6. - 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. 

All states and the District of Columbia have enacted laws setting 21 as the minimum drinking age. The table shows the estimated cumulative number of lives these laws have saved by reducing traffic fatalities.

Year	1995	1996	1997	1998	1999	2010
Lives(1000s)	15.7	16.5	17.4	18.2	19.1	?

Step-by-Step Solution

Answer

a.

b. A predicted equation is $y=0.85x+1680.1$

c. At 2010 year, total lives $28.4$ (in thousands)

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.

Take Years at the x axis and Lives at the y-axis, we get:

$(1995,15.7) , (1996,16.5),(1997,17.4),(1998,18.2),(1999,19.1)$

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 $(1996,16.5) and (1998,18.2)$

$\begin{array}{l}Slope=\frac{18.2-16.5}{1998-1996}[\because \text{ Slope =}\frac{y_2-y_1}{x_2-x_1}]\\ =0.85\end{array}$

Step-3 – Determine the equation.

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

Substituting values

 $\begin{array}{l}(y-16.5)=0.85(x-1996)\\ y-16.5=0.85x-1696.6\\ y=0.85x+1680.1\end{array}$

Hence, a predicted equation is $y=0.85x+1680.1$

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

Step-3 – Calculation

 $\begin{array}{l}y=0.85x-1680.1\\ y=0.85\left(2010\right)-1680.1\\ y=28.4\end{array}$

 Hence, the missing value is $y=28.4$ (in thousands)