# Slope field primer

• Mar 29th 2011, 11:44 AM
Wolvenmoon
Slope field primer
Alright. I don't have a picture of it. What I'm given is a slope field from -1<x<1 and -1<y<1 and told to graph it for A. y(-0.5)=1 and B. y(0)=1.

What I don't understand is what the y(-0.5)=1 and y(0)=1 are asking. Is my line supposed to cross at x=-.5 and Y=1? What do I do with the rest of it then if I'm only given that single point?

Basically, how do I read a slope field and how do I start drawing in it?
• Mar 29th 2011, 12:10 PM
Ackbeet
If your differential equation y' = f(x,y) satisfies certain regularity conditions, then you're guaranteed a unique solution, which means, among other things, that no two integral curves will intersect. With slope fields, if you're asked to graph a solution of the DE on it, you start at the initial condition, say y(-0.5) = 1, and draw a curve such that the slopes in the slope field are always tangent to your curve. See here for an example. You're given two different initial conditions; if your slope field doesn't have any "intersections" in it, then you should get two separate integral curves (solution curves) for the corresponding DE. Does that make sense?
• Mar 29th 2011, 12:17 PM
TheEmptySet
Quote:

Originally Posted by Wolvenmoon
Alright. I don't have a picture of it. What I'm given is a slope field from -1<x<1 and -1<y<1 and told to graph it for A. y(-0.5)=1 and B. y(0)=1.

What I don't understand is what the y(-0.5)=1 and y(0)=1 are asking. Is my line supposed to cross at x=-.5 and Y=1? What do I do with the rest of it then if I'm only given that single point?

Basically, how do I read a slope field and how do I start drawing in it?

Here is a slope field
Attachment 21294

http://www.mathhelpforum.com/math-he...2&d=1301429501

One way to visualize this is to think of the slope field as the velocity of a river. Now if you drop a cork on the point given where will the current take it.
• Mar 29th 2011, 12:20 PM
Wolvenmoon
Okay, seeing the arrow points helped immensely. I just have | and \ and /s on mine.

So to cement it in my head, he's giving me points to start on. My graph always stays parallel to the lines in the slope field, and that's about all there is to it?
• Mar 29th 2011, 12:37 PM
Ackbeet
Quote:

Originally Posted by Wolvenmoon
Okay, seeing the arrow points helped immensely. I just have | and \ and /s on mine.

So to cement it in my head, he's giving me points to start on. My graph always stays parallel to the lines in the slope field, and that's about all there is to it?

Pretty much. There's a lot less to slope fields than meets the eye.

TES: For me your picture is broken. Any chance you could fix?
• Mar 29th 2011, 12:56 PM
TheEmptySet
Quote:

Originally Posted by Ackbeet
Pretty much. There's a lot less to slope fields than meets the eye.

TES: For me your picture is broken. Any chance you could fix?

Hmm it is working for me I will upload another copy here
Attachment 21295

http://www.mathhelpforum.com/math-he...5&d=1301432063
• Mar 29th 2011, 01:23 PM
Ackbeet
TES: Nice!