Question

What is a constant of proportionality of (4,8) (1,2) (-1,-2)

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.

to get the slope of any straight line, we simply need two points off of it, let's use hmmm (-1 , -2) and (4 , 8)

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-1)}}} \implies \cfrac{8 +2}{4 +1} \implies \cfrac{ 10 }{ 5 } \implies 2`