Question

What is the constant of proportionality for this relationship?

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.

and to get it, we only need two points off a line, hmmm let's use those two points in the picture below.

$(\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{4}}}\implies \cfrac{6}{4}\implies \cfrac{3}{2}$