Question

What is the constant rate of change for this linear function? (-2,-2) (3,-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.

hmmm now, if we look at the coordinates above, well, notice, the y-coordinates are the same -2, that means is a horizontal line, and thus it has an slope of "0", now, we can just go through the rigamarole of rise/run and get the same thing.

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-2 +2}{3 +2} \implies \cfrac{ 0 }{ 5 } \implies \text{\LARGE 0}`