Question

Find the slope of the line for each ramp.

Answer 1

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

`\stackrel{\textit{\LARGE Ramp 1}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{40}~,~\stackrel{y_2}{400})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{400}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{40}-\underset{x_1}{0}}} \implies \cfrac{ 400 }{ 40 } \implies 10 \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{\LARGE Ramp 2}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{60}~,~\stackrel{y_2}{300})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{300}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{60}-\underset{x_1}{0}}} \implies \cfrac{ 300 }{ 60 } \implies 5 \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{\LARGE Ramp 3}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{100}~,~\stackrel{y_2}{200})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{200}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{100}-\underset{x_1}{0}}} \implies \cfrac{ 200 }{ 100 } \implies 2`