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The scatterplot shows the relationship between the length of time $y$ , in hours, a certain bird spent in flight and the number of days after January $11$ , $x$ .

What is the average rate of change, in hours per day, of the length of time the bird spent in flight on January $13$ to the length of time the bird spent in flight on January $15$ ?

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Explanation

The correct answer is $\frac{9}{2}$ . It's given that the scatterplot shows the relationship between the length of time $y$ , in hours, a certain bird spent in flight and the number of days after January $11$ , $x$ . Since January $13$ is $2$ days after January $11$ , it follows that January $13$ corresponds to an x-value of $2$ in the scatterplot. In the scatterplot, when $x equals 2$ , the corresponding value of $y$ is $6$ . In other words, on January $13$ , the bird spent $6$ hours in flight. Since January $15$ is $4$ days after January $11$ , it follows that January $15$ corresponds to an x-value of $4$ in the scatterplot. In the scatterplot, when $x equals 4$ , the corresponding value of $y$ is $15$ . In other words, on January $15$ , the bird spent $15$ hours in flight. Therefore, the average rate of change, in hours per day, of the length of time the bird spent in flight on January $13$ to the length of time the bird spent in flight on January $15$ is the difference in the length of time, in hours, the bird spent in flight divided by the difference in the number of days after January $11$ , or $\frac{15 - 6}{4 - 2}$ , which is equivalent to $\frac{9}{2}$ . Note that 9/2 and 4.5 are examples of ways to enter a correct answer.