Accelerating in Space vs Standing in Gravity Well

[Vosh]

Does this mean that if I have a line with a dot going from left to right and as I move the line up it traces a diagonal line, then if the dot accelerates, that diagonal line becomes curved?

I know my questions seem odd and it's hard to tell what I understand and don't understand; but I have to approach this in my own way... Many thanks.

 

[Vosh]

So if now instead of accelerating, my dot is placed near a planet and I have a line with a hump in it, this means that my dot is moving in a straight line in space, like the straight line at the equador, does the dot accelerating towards the planet translate as the dot moving further and further ahead in spacetime as it goes up the hump...?


I'm a dimwit, but bare with me.