Question

Find the average rate of change of the function defined by the following table

x I y
---------------
-2 I -5
2 I 35
6 I 75
10 I 115

Answer 1

in short, the average rate of change is plainly the slope of the set, so we can pick any two points off there, say 2, 35 and 10, 115,


`\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{35})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{115}) \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{115-35}{10-2}\implies \cfrac{80}{8}\implies 10`