Question

Find the rate of change for the situation. You run 14 miles in two hours and 28 miles in four hours.

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.

`\begin{array}{ccll} \stackrel{x}{miles}&\stackrel{y}{hours}\\ \cline{1-2} 14&2\\ 28&4 \end{array}\qquad \qquad \begin{array}{llll} (\stackrel{x_1}{14}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{28}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{28}-\underset{x_1}{14}}}\implies \cfrac{2}{14}\implies \cfrac{1}{7} \end{array}`