All right, so let's continue by learning how to calculate the slope of a line. You guys might remember this from algebra. Right. Um So here in the green box, I've got our our formula for slope, it's going to be our rise over run. Um The change in Y over the change in X Y two minus Y one over X two minus x one. These all mean the same thing in this class. It's probably not gonna get so algebra heavy. So we're just going to stick with rise over run for now. Cool. So let's go ahead and calculate a few examples here and see how this formula works. So let's start with this first graph a with the red line. Um And my first step when I'm calculating slope on a graph is I try and find two points that intersect on the graph, directly on one of these intersections on the graph. This first graph actually has quite a few of them. Um So, you know, right here, right here, right here, right. Some of our other examples won't be so easy to find those points, but the idea is we're gonna pick two of those points and we're gonna calculate our slope. So I'm gonna go ahead and pick this point and this 20.0.2 points uh that intersect the line there and let's go ahead and calculate the rise first. And then we'll do the run. So to calculate the rise, we have to see what the change in the vertical axis is, What is the change in the y value? So if we start here, we want to see what, how much did the up and down change for between these two points. So we started here at five and it looks like the next point is down here on four. Right? So it looks like we went down one and when we're calculating slope down is going to be negative and up is positive. Um just like when we're going left and right, left is negative and right is positive. I'll write that all down here, I'll put it here on the left hand side for you. So up is going to be positive and right is going to be positive, down is going to be negative and left is going to be negative up into the right is positive. Cool. Um So in our example here, like I said, we went down one, so that is going to be a slope of negative one. Excuse me not a slope of negative one. A rise of negative one. Now let's see what the run is. So from one point to the next, the x value seems to have shifted 1, 2 right here. So when it goes to the right, it's positive, right? We've got a positive one for the run. So let's go ahead and calculate the slope here, we've got slope and I'll write it rise over run. So our rise in this case was negative one. Our run was one. So that's going to simplify to negative one. Our slope here is negative one. Um, if you guys have a little, need a little refresher with fractions as well. I'm also including a fractions review uh, in this section too cool. So let's move on to part B here and let's calculate the slope here. I'm gonna get out of the way so we can see the example. And let's go ahead. Remember, like I said, the first step, we want to find two points that are intersecting the graph uh, at one of those intersections, right? So you can see in this, in this case we've got a few points here that don't exactly cross at those intersections. We want to find the two points or any two points that are crossing. It just makes it easier to calculate. So right here in the middle we've got one point and I'm gonna pick this one right here on the end and we're going to calculate the slope between those two points. So let's first do the rise the rise in this case. So it looks like we started at a vertical value of two, and the next point is at a vertical value of three. So let's see, we're gonna draw our arrow here and it looks like it went up one from 2-3. So I will write one right here and now let's do our run. So we started at three and we went to six. So it looks like our change was three here, right from 3 to 6 are run is three. So let's go ahead and calculate the slope slope again. I'll write it here rise over run. And in this case our rise was one are run was three and that's it. The answer is one third. The slope of this line is one third. So let's scroll down here. Um We've got one more graph, part C. And let's go ahead and calculate this slope. So I guess I'll come back so you don't feel so lonely? Hey guys, alright, so let's do part C again. We want to find two points where it's intersecting directly uh there on the graph. So notice kind of a point like that. They're not so easy to calculate. So let's find the easy points. I'll do in blue. We've got one right here and one right here, there's other ones. But those are the ones I'm gonna use. Cool. So let's start with our rise again. In this case we start at four, our next vertical value is six. So it looks like we're gonna go up here and it looks like we went up to right, we started at four, went to six. So our rise was to do the same thing with our run in this case it looks like we started at three and we got to four. So it looks like our run is going to be one in this case. And let's calculate the slope. So our slope again rise over run right. And our rise was to r run was one to over one. That's just too. So our slope in this case is too So let's go ahead and compare uh just let's look at these lines and see the difference in the slope and what the line looks like. So in part a we've got a negative slope, right, Our slope was negative one and notice how this line looks compared to the other lines, right? It looks like when we go from left to right, it looks like this uh this line is going downhill right, because the slope is negative, it forms a downhill right going from left to right and notice our other two which have positive slopes, they look like they're going uphill right, B and C both have this uphill tendency. But now let's look at one more thing here, notice and be our slope was one third and see our slope is too right. So too is quite a bit bigger than one third. And look at how these lines look right and be you kind of see like a soft growth here, right? It's kind of a little bit of an uphill where in see where we have a slope of two. It's a lot steeper. So the higher the slope is the steeper it's going to get this way and if it was a really negative number. So if a was negative to you could imagine it would be a lot steeper going down. Cool, Alright, so that's how we calculate slope. Let's move on.