Relationships between Variables - Video Tutorials & Practice Problems

Drawing and Shifting Curves

So now we're gonna learn how to take points on the graph and turn them into a curve as well as how to shift that curve on the graph. We're also gonna learn how to shift curves just visually with no math, the tool use quite often in this class. So let's go ahead and look on the graph here. You'll see I have the points from the previous video where we learned how to put points on the graph. I've got those points here already. So when we're turning points into a curve, um what we do is we start at the left most point and we work our way right words. Okay. Um This one seems pretty simple, it's just gonna make a line and yes, a line is a curve, it's just a straight curve. So this is what this curve may look like right here in green. Alright. Um I just want to make an example here. I'm gonna do something right here on top. Let's say we had points that looked like this, ignore the other points right now. But let's say there were points like this, there's a specific way we want to connect those right? We want to start left to right, just like I said um you never want to double back and start going back to the left there back to the right. Um Let me show you in an example here, right? So these points we would connect them something like this right? And I don't want you to get confused and connect them. Maybe like this right? That's not how we would connect these points. Um you start at the left most point and you go to the right. Cool. So now let's talk about shifting this green curve right here. How do we shift it on the graph? Let's say someone told us we had to shift this curve, let's say two units to the right, two units to the right. Okay. So how do we do that, what we're gonna do? And the easiest way I find to do it is I pick the left most point. So in this case it would be this point that I'm gonna circle here in black right and we're gonna move it two spaces to the right, so I'm gonna count here. Two, that's one and that's two right there. That's gonna be our new point that I'll put in blue. Cool. So you do that with your left most point and I'd like to just go straight to the right most point and do the same thing, grab my pen And I'll pick this right most point right down here and I'm gonna move it two spaces to the right one to write and I'm gonna put my point right there, my new point and now that I have two points. Um if you just connect these two points you'll have your new line so I'll do that one in green as well. So here we go connecting these two points, we've got our shifted curve. So this new green curve right here, it's shifted to the right, Actually, I'm gonna do it in blue so we can see which one's which. So blue curve has been shifted to to the right. Cool. And a lot of times in this class, like I said, we're gonna be doing shifting of curves just visually, we're not going to put any math behind it, we're gonna have a reason, we're shifting the curve and then we're gonna have to see what happens after we've shifted the curve. Um And when I say, see what happens, we're gonna see what happened to the new price and the new quantity. Um but we'll get more into that in the next chapter. So I'm gonna draw a couple of graphs here just to explain what I mean by shifting visually. So a lot of times on a test or on a practice problem, you're just gonna kind of draw a graph kind of willy nilly like this, and a lot of them are gonna be graphs that look like this, we're gonna have an X. And remember I suggested having at least two colors. Um and we're gonna use those quite often. So in this case, um what we're gonna do is kind of like we did above on the graph, we're gonna shift the red line to the right, so now it's not two units, we're just shifting to the right, cool. So what you do is you start and you're going to pick a point on the graph, you're gonna move it to the right and then you're going to draw a parallel line just like that. Right? So when we do these kinds of shifts, what we're doing is looking for these points of intersection where this was the point of intersection originally. Now we're at this point of intersection here. Right? So we would be judging what happened to the price and what happened to the quantity after this shift. Right. So we can make assessments of that just visually without doing any math. Um but we'll deal more with analyzing it when the time comes. Now, I'm just trying to expose you to shifting the graphs like that. So let's do a couple more examples here. Now let's shift the red line to the left. So we're gonna start with the red line and you can see now if I went to the left, I kind of end up off the graph here. Right? So maybe I can pick a point like a little further down and go to the left here and now I can draw a parallel line. Right? So you just want to make sure you're going the correct direction and let's see where our new intersection is. We were here before and now we've moved down there. Right? So we will be able to make assessments about price and quantity based on that movement. Cool. A couple more examples here. So now let's move the blue line. Let's see what happens when we move the blue line to the right. So same thing, we're gonna pick a point here, move it directly to the right and draw a parallel line. Cool. So the point of intersection was there and now it's there. All right. Now let me get out of the way. I'm gonna do one more example here in this last corner. So sometimes we actually have to shift both the lines on the same graph and that's when it starts to get a little difficult remembering which line was which. So I like to draw my ex so that the original point of intersection is right in the middle, right? When I'm doing it visually I just keep that point of intersection in the middle. And then I'm gonna look at my new points of intersection. So let's say we had to move um let's just move them both to the right in this example. So first let's move the red line to the right. So I'm gonna pick a point here, move it to the right and draw my new line. And now I'm gonna draw the blue line. We're also gonna shift to the right. So pick a point, go to the right and draw my new line. So you can see now there's a lot of points of intersection here, it's like which one is the new one, which one is the old one. So you gotta be careful and pick the correct intersection here. So you want to have good eyes at finding these because this is gonna happen quite a bit in this class when we're studying demand and supply. So which one did you pick? This is gonna be our new point of intersection right here? Let me go. Yeah, I'll leave it in green. So we see that that's the new point of intersection right there. Cool. Um So this is how we're gonna shift curves visually on the graph and we can also do it mathematically like we did on the left. But mostly we're gonna do it like we did on the right in this course. See you in the next video.