Question

A car travels 2 1/3 miles in 3 1/2 minutes at a constant speed. Write an equation to represent the constant of proportionality.

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.

the assumption here being that if we were to graph the traveling of the car the miles will be on y-axis usually whilst the minutes on the x-axis usually, so is simply asking for the slope, and since the car began at 0 miles at 0 minutes, at the origin of our graph, then the rise and run are pretty much those values above.

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3(1)/(2)}~,~\stackrel{y_2}{2(1)/(3)}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2(1)/(3)}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{3(1)/(2)}-\underset{x_1}{0}}} \implies \cfrac{ ~~ 2(1)/(3) ~~ }{3(1)/(2)}\implies \cfrac{~~ ( 7)/(3 ) ~~}{(7)/(2)}\implies \cfrac{7}{3}\cdot \cfrac{2}{7}\implies \boxed{\cfrac{2}{3}}`