Now let's learn how to find equilibrium using just a little bit of algebra, and I know I scared you there with that nasty word I just dropped, but I promise you that algebra is not going to get so intense in this segment, alright? There's just going to be a little bit of formula rearranging and solving, so it's going to be pretty basic and I'll do some reviews as we go along, so hopefully, you'll get a good hang of the kind of algebra we'll need. So let's start with the demand curve here. Sometimes you can be given an equation for a line like you see here, \( p = 800 - 2 \times \) quantity demanded, right? And the easiest way to take this information and be able to put it on a graph is to just pick some values for the quantity here and we'll solve for price, right? We'll pick values for quantity because it's on the right-hand side and price is already by itself, so it'll be a lot easier to just solve for price in that situation. So let's go ahead and start with a very easy value for quantity. Why don't we start with the value of 0? What if the quantity is 0? Let's go ahead and see what happens in our equation. \( P = 800 - 2 \times 0 \) that's going to disappear, so we're going to end up with \( P = 800 \), right? That is going to be our price. When the quantity is 0, the price is going to be 800. So if people, if the market is charging a price of 800, there will be 0 quantity demanded. Let's go ahead to our graph and let's plot this point. So we've got our price axis over here, our quantity axis over here, alright? And let's take that point. So we have a quantity of 0, which is right here along the line and let's go ahead and, mark the price of $800. So at a price of $800 up here, I'm going to use I'll use blue. Price of $800, we're going to have a quantity demanded of 0. Alright, let's go ahead and pick some other quantities. So how do we go about picking the quantity we're going to use? Well, you want it to be something that's going to be easy to put on your graph, right? Our graph is already quantities of 100, 200, 300, so I'm going to go ahead and just pick a quantity of 200 now. Okay, because I know I'll be able to find that easily on the graph. Okay. And you can pick any number. You could pick 6 right now, but I think it'd make it a lot more difficult to graph. So I'm going to pick a number 200. Let's go ahead and plug that into our equation. So quantity of 200, \(p = 800 - 2 \times 200 \). So that's going to be \( p = 800 - 2 \times 200 = 400 \), and \( p \) is going to equal 400. So with a price of 400, quantity demanded will be 200. Let's go ahead and get that on our graph. Price 400, quantity demanded 200 will be somewhere right here. Alright, let's, and by the way, right now, with these two points, we can make our demand curve, right? It's going to be a straight line, so we know that our curve is going to be like this, right? Something like that. It's going to pass through both of those points. I guess I could draw a little better. Let me try one more time here. Oh, I missed the other way now. One more. Alright. That was a little better. So there we go. That's what our demand curve is going to look like, but it doesn't hurt to do an extra one. We can always just confirm what we were doing here. So let's go ahead and pick a quantity of 300, right. It looks like at 300, we're going to be at this 200 price level, right? That's where it looks like it's going to cross. Let me erase those. So let's go ahead and see if that's the answer we get. Price or quantity of 300, let's solve for price. \( P = 800 - 2 \times 300 \). \( P = 800 - 2 \times 300 = 200 \), and sure enough, we got a price of 200 here. Right? So there it is. We got that answer. Feel pretty good about our line. So that is what our demand curve is going to look like here. Alright? So now I want to do a quick recap of how we can isolate different variables, and let's go ahead and do that in the next video.