Metro Department Store's annual sales (in millions of...

Metro Department Store's annual sales (in millions of dollars) during the past 5 years were $$\begin{array}{lccccc} \hline \text { Annual Sales, } y & 5.8 & 6.2 & 7.2 & 8.4 & 9.0 \\ \hline \text { Year, } x & 1 & 2 & 3 & 4 & 5 \\ \hline \end{array}$$ a. Plot the annual sales ( $y$ ) versus the year $(x)$ b. Draw a straight line $L$ through the points corresponding to the first and fifth years. c. Derive an equation of the line $L$ d. Using the equation found in part (c), estimate Metro's annual sales 4 years from now $(x=9)$

Metro Department Store's annual sales (in millions of dollars) during the past 5 years were
$$\begin{array}{lccccc}
\hline \text { Annual Sales, } y & 5.8 & 6.2 & 7.2 & 8.4 & 9.0 \\
\hline \text { Year, } x & 1 & 2 & 3 & 4 & 5 \\
\hline
\end{array}$$
a. Plot the annual sales ( $y$ ) versus the year $(x)$
b. Draw a straight line $L$ through the points corresponding to the first and fifth years.
c. Derive an equation of the line $L$
d. Using the equation found in part (c), estimate Metro's annual sales 4 years from now $(x=9)$

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Key Concepts

Scatter Plot

A scatter plot is a graphical representation where each point on a Cartesian coordinate system corresponds to a pair of values. It is used to display the relationship between two variables, allowing for visual inspection of trends, patterns, or potential correlations.

Two-Point Formula

The two-point formula is a method used to determine the equation of a straight line when two points on the line are known. It involves calculating the slope by taking the difference in the y-coordinates divided by the difference in the x-coordinates and then using one of the points to formulate the line’s equation.

Linear Equation Formulation

Formulating a linear equation typically involves expressing the relationship between two variables in the form y = mx + b, where m is the slope and b is the y-intercept. This equation provides a mathematical model for the data, facilitating calculations and predictions.

Extrapolation

Extrapolation is the process of using an existing model, like a linear equation, to estimate values outside the range of the observed data. It is a common forecasting technique where the underlying assumption is that the established pattern continues beyond the given data points.

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