Question

What is the average rate of change for the sequence shown below? coordinate plane showing the points 1, 2; 2, 2.5; 3, 3; 4, 3.5; and 5, 4

Answer 1

Answer: The average rate of change is $\frac{1}{2}$

Step-by-step explanation:

 The points (1, 2); (2, 2.5); (3, 3); (4, 3.5) and (5, 4) belong to the line shown in the graph attached.

The average rate of change for the sequence is the slope and you can calculate it with the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Then, choose two points of the line and substitute them into  $m=\frac{y_2-y_1}{x_2-x_1}$:

Let's choose the point (1,2) and the point (2,2.5). Then:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{2.5-2}{2-1}\\\\m=\frac{1}{2}$