Question

Match each pair of points, to the slope of the line between them. (1,3) and (5,6) (1,7) and (5,4) (5,5) and (2,1)

answers 4/3,-4/3,3/4,-3/4​

Answer 1

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ 3 }{ 4 } \implies \cfrac{3}{4} \\\\[-0.35em] ~\dotfill`

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3}{4} \\\\[-0.35em] ~\dotfill`

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -4 }{ -3 } \implies \cfrac{4}{3}`