Question

Which function , A or B has a greater rate of change ? Be sure to include the values for the rates of change in your answer . Explain your answer in words please .

Answer 1

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:

$Rate \ of \ Change=\frac{Change \ in \ y}{Change \ in \ x}$

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 $(1,5) \ and \ (2,7)$:

$ROC=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ ROC=\frac{7-5}{2-1} \\ \\ ROC=\frac{2}{1} \\ \\ \boxed{ROC=2}$

FOR THE GRAPH:

Let's take $(1,1) \ and \ (2,4)$:

$ROC=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ ROC=\frac{4-1}{2-1} \\ \\ ROC=\frac{3}{1} \\ \\ \boxed{ROC=3}$

As you can see, $3>2$ so the ROC of the function given by the graph is greater than the ROC of the function given by the table.