Question

The line L passes through the points (1,2) and (-4,-4)
Find the gradient of line L

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}{1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{1}}}\implies \cfrac{-6}{-5}\implies \cfrac{6}{5}`