Question

I really need help with this ​

Answer 1

Check the picture below.

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.

how fast is it traveling? or what's its average rate or slope?

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{4}}} \implies \cfrac{ 4 }{ 2 } \implies \cfrac{2~meters}{1~second}\qquad \textit{2 meters per second}`