Question

A line segment is drawn between (2,8) and (5,4). find it’s gradient.

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.

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\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}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{4 }{ 3 }`