Question

The coordinates of three points are A(-6, 4), B(4, 6) and C(10, 7).

Find the gradient of AB and the gradient of BC.

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.

`A(\stackrel{x_1}{-6}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-6)}}} \implies \cfrac{ 2 }{4 +6} \implies \cfrac{ 2 }{ 10 } \implies \cfrac{1}{5} \\\\[-0.35em] ~\dotfill`

`B(\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{10}~,~\stackrel{y_2}{7}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{4}}} \implies \cfrac{ 1 }{ 6 }`