Question

What is the average rate of change over the interval [-1,2]​

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so let's take a peek at the table, so hmmm when x = -1, b(x) = 1, so we have the point (-1 , 1), and when x = 2, b(x) = 7, so we have the second point of (2 , 7)

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{7}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}}\implies \cfrac{6}{2+1}\implies \cfrac{6}{3}\implies 2`