Question

The table below shows the linear relationship between the number of cookies in the cookie jar and the days that have passed.

What is the rate of change of the number of cookies with respect to the time in days? answer choices - 4,5,-5,-4

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}{2}~,~\stackrel{y_1}{26})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{16}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{16}-\stackrel{y1}{26}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -10 }{ 2 } \implies -5\qquad \begin{array}{llll} \textit{5 cookies less per}\\ \textit{every passing day} \end{array}`