Question

Find the gradient of a line passing through the coordinates A(3;9) and B(4;-1)​

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}{3}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{3}}} \implies \cfrac{ -10 }{ 1 } \implies - 10`