Use the Midpoint Formula to estimate the sales of Big Lots,...

Use the Midpoint Formula to estimate the sales of Big Lots, Inc. and Dollar Tree Stores, Inc. in $2005,$ given the sales in 2003 and 2007 . Assume that the sales followed a linear pattern. (Source: Big Lots, Inc.; Big Lots$$ \begin{array}{|c|c|} \hline \text { Year } & \text { Sales (in millions) } \\ \hline 2003 & \$ 4174 \\ 2007 & \$ 4656 \\ \hline \end{array} $$

Use the Midpoint Formula to estimate the sales of Big Lots, Inc. and Dollar Tree Stores, Inc. in $2005,$ given the sales in 2003 and 2007 . Assume that the sales followed a linear pattern. (Source: Big Lots, Inc.;
Big Lots$$
\begin{array}{|c|c|}
\hline \text { Year } & \text { Sales (in millions) } \\
\hline 2003 & \$ 4174 \\
2007 & \$ 4656 \\
\hline
\end{array}
$$

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Key Concepts

Midpoint Formula

The Midpoint Formula is a mathematical formula used to determine the point that is exactly in between two given points in a coordinate plane. It involves averaging the x-coordinates and y-coordinates of the endpoints separately. In the context of linear data, it provides a simple method to estimate a value at the midpoint of two known values.

Linear Function

A linear function models a relationship between two variables with a constant rate of change, forming a straight line when graphed. In problems involving estimation between two data points, the assumption of linearity means that the changes between points occur uniformly, which makes techniques such as averaging applicable.

Interpolation

Interpolation is the process of estimating unknown values within the range of a set of known data points. When the relationship between the data points is assumed to be linear, as in this type of problem, both the midpoint formula and linear interpolation techniques can be used to provide an estimated value at a point within the interval.

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