Question

What is the average rate of change for f ( x ) = 0 . 5 ( − 10 x + 24 ) f x = 0 . 5 - 10 x + 24 ?

Answer 1

bearing in mind that the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

`\bf f(x) = 0.5(-10x+24)\implies f(x) = \stackrel{\stackrel{m}{\downarrow }}{-5} x+12\impliedby \begin{array} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}`