How do I determine behavior of y at infinity for a given differential equation?

[Punchlinegirl]

Draw a direction field for the given differential equation. Based on the the direction field, determine the behavior of y at t goes to infinity. If this behavior depends on the initial value of y at t=0, describe the dependency.
y'= -1-2y


In class we did examples where we had a range. Like we were given y'=2y-3 and told to draw the direction field for -2<y<2 and -2<t<2.
So for the problem above, how would I find a range, since it wants to infinity?

 

[HallsofIvy]

"t going to infinity" doesn'g mean anything here. Your direction field is a graph in an xy-coordinate system and t doesn't have anything to do with it. At every (x, y) point, you want to draw a short vector having slope
$\frac{dy}{dx}$. But you are told that the slope is -1- 2y which depends on x only. Should be easy to draw.