Answer:
7.34 cubic inches per inch
Step-by-step explanation:
Average Rate of Change
Average rate of change or slope measures the change in y over the change in x.
[tex]\text{slope}=\dfrac{\Delta y}{\Delta x}[/tex]
In words, it shows how fast or how slow something is increasing or decreasing relative to the independent variable (along x-axis).
[tex]\hrulefill[/tex]
Solving the Problem
We're told to find the slope between 0.5 and 1 inch.
Inspecting the graph, we can deduce that the independent variable or x-axis are in length (inches) and the dependent variable or y-axis are in volume.
Additionally, we see that the graph highlights two coordinate points, one with 0.5 inch and its correlating volume and the other with 1 inch and its correlating volume.
The difference between the y-values is 4.19 - 0.52 or 3.67; the difference between the x-values is 1 - 0.5 or 0.5.
Thus the slope is 3.67 / 0.5 or 7.34.
