Question

Brandon is on a diet. The graph

above shows his weight from the
start of the diet. Find the rate
of change from the sixth week
to the eighth week.

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.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{194})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{178}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{178}-\stackrel{y1}{194}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{6}}} \implies \cfrac{ \stackrel{Lbs}{-16 }}{ \underset{Weeks}{2} } \implies \cfrac{\stackrel{Lbs}{-8}}{\underset{Weeks}{1}}\implies {\Large \begin{array}{llll} -8~(Lbs)/(Week) \end{array}}`