Answer:
A rate of change tells us how one quantity changes in relation to another quantity. In a mathematical language, we can write this as follows:
[tex]Rate \ of \ Change=\frac{Change \ in \ y}{Change \ in \ x}[/tex]
For linear functions. the rate of change is the slope of the line. Thus:
FOR THE TABLE:
By taking two points we can get the rate of change, so let's take [tex](1,5) \ and \ (2,7)[/tex]:
[tex]ROC=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ ROC=\frac{7-5}{2-1} \\ \\ ROC=\frac{2}{1} \\ \\ \boxed{ROC=2}[/tex]
FOR THE GRAPH:
Let's take [tex](1,1) \ and \ (2,4)[/tex]:
[tex]ROC=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ ROC=\frac{4-1}{2-1} \\ \\ ROC=\frac{3}{1} \\ \\ \boxed{ROC=3}[/tex]
As you can see, [tex]3>2[/tex] so the ROC of the function given by the graph is greater than the ROC of the function given by the table.
