Alright. So now we're gonna learn how to calculate the slope of a curve when it's not a straight line. So the idea here on this, on this graph, what you see is a curve um that's not straight, but in this situation, how do we calculate the slope? So when you see a curve like this, the slope is actually changing all the time. Um So you're gonna have a different slope at this point where it's rising pretty fast then at this point where it's kinda going up a little slower, right, you would imagine from our last video that those would have two different slopes. So the first method when calculating the slope of of a curve is to use what's called the point method. And what we do is we draw a tangent line right? Um uh We draw a tangent line. So a tangent line touches the curve at only one point. Okay, so the idea is we're going to calculate the slope of the line at that point on the graph. Cool. So once we draw the tangent line we just calculate the slope of the tangent line and then we know what the slope is at that point. So I'm gonna go ahead and do my best to draw a tangent line. It's not very easy to do this by hand. Um If you were ever to have to calculate this in this class, I'm sure they would give you the tangent line already. Um And I'll do my best here should look something like that. So the idea is that it's only touching the graph at one point even if it doesn't look like it from my example I did my best but the idea is that it's only touching the graph right there. So the tangent line is just going going going, it touches the graph and it keeps going just one one point that it touches the graph. So now that we have a tangent line we can go ahead and calculate the slope of the tangent line and we will know the slope at that point. So um using our same method from finding the slope, let's find to points that intersect the graph. Um And it'll make it easier to calculate. So I see one there um here's another one right here let's go ahead and calculate that slope. So um it looks like from the first point to the second point we are going up right let me do this in a different color. We'll do it in green. Um It looks like we're going up and from that point to that point we went up from 4 to 6. So it looks like our rise was two. And let's do our run now. So it looks like we started with an X. Value of three. We got to an X. Value of five. So our run was also too. So let's calculate this slope. So the slope of the tangent line. I'll put slope of tangent line equals still that rise over the run. And in this case we've got a rise of two, a run of two and that simplifies to over two simplifies to one. So the slope of the tangent line is one. And that means that the slope at this point where we drew the tangent line right here, the slope of that point equals one. So the slope of that curve at that point is one. Remember it's constantly changing, but at that point the slope is one. So that is how we calculate the slope of a curve. Using the point method, let's move on to the next video.