A movie theater has kept records of popcorn sales versus...

A movie theater has kept records of popcorn sales versus movie attendance. (A). Use the table to write the corresponding ordered pairs using the movie attendance as the $x$ -variable and sales of popcorn as the $y$ -variable. Interpret the meaning of the first ordered pair. (see Example 4 . (B). Plot the data points on a rectangular coordinate system. $$\begin{array}{c|c} \begin{array}{c} \text { Movie Attendance } \\ \text { (Number of People) } \end{array} & \begin{array}{c} \text { Sales of } \\ \text { Popcorn (S) } \end{array} \\ \hline 250 & 225 \\ \hline 175 & 193 \\ \hline 315 & 330 \\ \hline 220 & 209 \\ \hline 450 & 570 \\ \hline 400 & 480 \\ \hline 190 & 185 \\ \hline \end{array}$$

A movie theater has kept records of popcorn sales versus movie attendance.
(A). Use the table to write the corresponding ordered pairs using the movie attendance as the $x$ -variable and sales of popcorn as the $y$ -variable. Interpret the meaning of the first ordered pair. (see Example 4 .
(B). Plot the data points on a rectangular coordinate system.
$$\begin{array}{c|c}
\begin{array}{c}
\text { Movie Attendance } \\
\text { (Number of People) }
\end{array} & \begin{array}{c}
\text { Sales of } \\
\text { Popcorn (S) }
\end{array} \\
\hline 250 & 225 \\
\hline 175 & 193 \\
\hline 315 & 330 \\
\hline 220 & 209 \\
\hline 450 & 570 \\
\hline 400 & 480 \\
\hline 190 & 185 \\
\hline
\end{array}$$

Key Concepts

Ordered Pairs

Ordered pairs are a method of representing data where each pair (x, y) corresponds to two related pieces of information. In the context of data tables, one value serves as the independent variable (typically the x-value) and the other as the dependent variable (the y-value). This notation allows us to clearly specify the relationship between the two measured quantities.

Independent and Dependent Variables

When analyzing data, the independent variable is the factor that is presumed to influence or predict the dependent variable. The dependent variable is the outcome or response that is measured. Understanding this relationship is crucial for interpreting how changes in one variable might affect another, and it directs how we construct our data representations, such as ordered pairs and graphs.

Cartesian Coordinate System

The Cartesian coordinate system provides a framework for graphing data in a two-dimensional space using a horizontal axis (x-axis) and a vertical axis (y-axis). Every ordered pair is plotted as a point on this grid, enabling visual analysis of the relationship between the independent and dependent variables. This fundamental tool helps in identifying trends, patterns, or correlations in the data.

Data Visualization (Scatter Plot)

A scatter plot is a type of graph that is used to display data points from two variables plotted on a Cartesian coordinate system. Each plotted point represents an observation defined by its ordered pair. Scatter plots are particularly useful for detecting patterns, clusters, or possible outliers, thereby providing insights into the nature and strength of the relationship between the variables.

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