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	?

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.

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

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

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

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

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

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 $y=0.85x+1680.1$

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

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

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

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