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.
so the speed in this case will be the rate of change or namely the slope, hmm 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 for both intervals
![\stackrel{ \textit{first 15 minutes} }{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{1})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{0}}} \implies \cfrac{ 1 }{ 15 } \implies \cfrac{1}{15} ~~ \cfrac{km}{min}\qquad 0.0\overline{66}~km/m \\\\[-0.35em] ~\dotfill](https://img.qammunity.org/2024/formulas/mathematics/college/7fvgnyb7tnk7vkwycmdd6wnbkcxzi693yv.png)
