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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Medium

During a study, the temperature, $in degrees Celsius (° C)$ , of the air in a chamber was recorded to the nearest integer at certain times. The scatterplot shows the recorded temperature $y$ , $in ° C$ , of the air in the chamber $x$ minutes after the start of the study.

What was the average rate of change, $in ° C$ per minute, of the recorded temperature of the air in the chamber from $x equals 5$ to $x equals 7$ ?

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Explanation

The correct answer is $5$ . For the graph shown, $x$ represents time, in minutes, and $y$ represents temperature, in degrees Celsius $(° C)$ . Therefore, the average rate of change, in $° C$ per minute, of the recorded temperature of the air in the chamber between two x-values is the difference in the corresponding y-values divided by the difference in the x-values. The graph shows that at $x equals 5$ , the corresponding y-value is $14$ . The graph also shows that at $x equals 7$ , the corresponding y-value is $24$ . It follows that the average rate of change, in $° C$ per minute, from $x equals 5$ to $x equals 7$ is $\frac{24 - 14}{7 - 5}$ , which is equivalent to $StartFraction 10 Over 2 EndFraction$ , or $5$ .