Question

Help please I need to turn this in soon

Answer 1

as you already know, the average rate of change is namely the slope in a function, thus, let's pick any two points from that table to get its equation.

`\bf \begin{array}cc \cline{1-2} minutes&altitude\\ \cline{1-2} 1&35000\\ \underline{2}&\underline{31000}\\ 3&27000\\ \underline{4}&\underline{23000}\\ \cline{1-2} \end{array}~\hspace{7em} (\stackrel{x_1}{2}~,~\stackrel{y_1}{31000})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{23000}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{23000-31000}{4-2}\implies \cfrac{-8000}{2}\implies -4000`

`\bf \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-31000=-4000(x-2) \\\\\\ y-31000=-4000x+8000\implies y=-4000x+39000`

Answer 2

Option #2

if m=1

a=-4000m+39,000
a = -4000(1) + 39,000
a= -4000 + 39,000
a=39,000-4000
a=35000

if you plug m in you'll find it matches with what a is on the other side of the table