So in physics, some of the most common graphs that you'll see are graphs of lines, and one of the most important variables you'll have to solve for is the slope of lines. Let's go ahead and talk about that real quick. The slope, remember, is just a number that represents how steep the line is, sort of how vertical it is. The green line kind of looks like this. The red line is a little bit steeper, so it's going to have a higher slope. Mathematically, what's going on is just the change in the y value divided by the change in the x value. One of the things you've probably heard before in some classes is rise over run, which is basically just the change in y over the change in x. We use this little delta symbol, which you will see a lot in physics, to describe the change in a variable.

So, real quickly here, if we want to calculate the slopes of these two lines on the graph, you just have to figure out the rise of the run. How much does it rise? Well, you're going from 2 to 4, so the change in y is just 2, and then you're going from 1 to 2 over here, so the change in x is just 1. So when you calculate the slope, it's just ΔyΔx, 2 over 1, and the slope is just a value of 2. Alright?

Let's do the same thing for the red line. All we're going to have to do here is just pick 2 points. I'm going to pick this point over here and this point and figure out the rise of the run. So if I have to go from this point to this point, first, I have to go up. And if you count up the number of units, you're actually going to end up going 5 units. That means my delta y is 5, then you have to go over by 1 unit over here. So delta x is 1. The slope in this case is 5 over 1, and this is 5. So just as we said before, this slope here, which is 5, is a higher number, and it just represents that the slope is steeper than this green line over here, which has a slope of 2. Alright? So that's all there is to slopes.