 Hello and welcome to a screencast today about using geotubra to generate a slope field. Alright, so the problem we're going to look at today is use geotubra to generate a slope field for our differential equation dy dt equals negative 2ty. Alright, let me minimize these and bring up, let me bring up geotubra here, minimize the stuff in the background so it doesn't distract us. Alright, so here is geotubra and down here in my input button I'm going to just start typing the word slope and you'll notice here slope field is one of the options that pops up. Okay, so instead of having that kind of, I don't know, they're less than or equal to signs but whatever you want to call those pointy brackets with the f of x, y and you notice that geotubra uses the variables x and y. Our differential equation used the variables t and y but it's okay, we can just replace the t with an x. So we've got negative 2xy and then when I hit enter, bam, there's my slope field. Okay, that's beautiful. So now I actually took this picture and I put it into my screencast so that way we actually have something we can look at. So depending on what the initial condition is of my differential equation, like let's say for example, I don't know, we're starting down here at negative 1 for whatever reason. So then you can kind of see how these slope fields run. So they kind of are, I don't know, if we start over here they're kind of decreasing, decreasing and then it kind of starts to, oops, that should have been a little bit more at the minimum there, and then it kind of starts to increase, increase, increase. So we've got some kind of a bell shaped curve here. Now let's say my initial condition had been up here in the positive area, like let's say, I don't know, about 1.5 and let me do this in a different color. So let's say my initial condition were up here. So then you can kind of see how my slope field is increasing, increasing, increasing, kind of hits my initial condition and then it's going to start to decrease, decrease, decrease. So we still kind of have that bell shaped curve. Alright, so remember there are infinitely many solutions to this differential equation. It just depends on your initial condition. But the slope field kind of gives us a feel for what the graph is going to end up looking like that is a solution to our differential equation. Alright, using GeoGebra helps a lot. I mean you can do these by hand as well as you'll see in another screencast. But using GeoGebra sure does make it easy. Alright, thank you for watching.