Show that: Delta Y = -5 x Delta X
Well, here's the thing...we don't show that $\displaystyle \Delta{y}=-5\Delta{x}$ because it just is. This is a trivial case.
I can try something, though...
In an amazing feat, I VonNemo19 will attempt to show that $\displaystyle \Delta{y}=-5\Delta{x}$
Are you ready?
Spoiler:
Seriously, though. We need some more info here.
Prove what? To prove something, we need some GIVEN information and that the result follows strictly from the given information. all you have is the result.
EG: Given $\displaystyle y=x^2$, show that $\displaystyle y'=2x$
See? Check your notes or something. Look for this mystery info that I speak of.
Slope - Wikipedia, the free encyclopedia
Read that. Oh, and don't forget to keep digging for that missing information.