Respuesta :
Alex made 1600 bucks in 400 hours... how much did he make in 0 hours? well, he just laying on a hammock, so he did 0 dollars then.
so,
[tex]\bf \begin{array}{ccll} \stackrel{x}{hours}&\stackrel{y}{dollars}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 0&0\\ 400&1600 \end{array} \\\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& 400~) % (c,d) &&(~ 0 &,& 1600~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1600-0}{400-0}\implies \cfrac{1600}{400}\implies \cfrac{4}{1}\implies 4[/tex]
now, let's take a peek at g(x)'s slope,
[tex]\bf \begin{array}{ccll} x&g(x)\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \underline{1}&\underline{-8}\\ 5&12\\ \underline{9}&\underline{32} \end{array}\impliedby \textit{let's pick two points}[/tex]
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 1 &,& -8~) % (c,d) &&(~ 9 &,& 32~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{32-(-8)}{2-1}\implies \cfrac{32+8}{9-1}\\\\\\ \cfrac{40}{8}\implies 5[/tex]
well, all we can say is that, they differ.
so,
[tex]\bf \begin{array}{ccll} \stackrel{x}{hours}&\stackrel{y}{dollars}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 0&0\\ 400&1600 \end{array} \\\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& 400~) % (c,d) &&(~ 0 &,& 1600~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1600-0}{400-0}\implies \cfrac{1600}{400}\implies \cfrac{4}{1}\implies 4[/tex]
now, let's take a peek at g(x)'s slope,
[tex]\bf \begin{array}{ccll} x&g(x)\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \underline{1}&\underline{-8}\\ 5&12\\ \underline{9}&\underline{32} \end{array}\impliedby \textit{let's pick two points}[/tex]
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 1 &,& -8~) % (c,d) &&(~ 9 &,& 32~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{32-(-8)}{2-1}\implies \cfrac{32+8}{9-1}\\\\\\ \cfrac{40}{8}\implies 5[/tex]
well, all we can say is that, they differ.
