Question

The plans for a zipline are shown. Use two points to determine the slope of the zipline. Then verify that the slope is the same by choosing a different set of points. Enter your answer as a fraction or decimal.

Answer 1

Check the picture below.

let's first use the two red points, and then the two purple points.

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{1}}} \implies \cfrac{ -2 }{ 6 } \implies -\cfrac{1}{3} \\\\[-0.35em] ~\dotfill`

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{4}}} \implies \cfrac{ -2 }{ 6 } \implies -\cfrac{1}{3}`