Slope of a Line - Part 1

The slope of a line is of is often described as rise over run, and is notated by the letter m. So m is the slope which is rise over run. What we mean by rise is how far we have to rise up to get from point to point. Also, by run, the same idea. So let's just plot two points and figure out what the slope is. Let's say, I've got a point here and a point, oh, let’s say here. So what I’m going to do is say that here's a line (I try to draw that as straight as possible), say here’s a line and I want to move from this point to this point. So what I must do is I have to figure out how much first I have to rise up. From here, I've got 1, 2, 3, 4. Four units up. Since it is a positive direction, meaning an "up" direction, we write it as a positive number, which is 4. Now to get over to the next point we have to move to the left, it looks like, 2 units. Our run is two, but notice in this direction it means that we're going in a negative direction along the x-axis. So, we must make this as a negative 2. We have 4 divided by negative 2 which is simply negative 2. Now you might be asking, "What's the difference between negative 4 divided by negative 2?" It's not really any different. It's basically how you move from one point to the other. If we wanted, we could start with this point here and move. It doesn't matter where you start as long as you get the signs and the directions correct. So let's say we're starting here and we have to go 1,2,3,4. Yes, we moved four units but notice the rise was in a negative direction. So we can say that our m is a negative 4, which is our rise, so we went in a negative direction. Then, from there, we have to move over to the right 2 units. Notice it's in a positive direction of x so, if it’s in a positive direction, that means it will be a positive 2. So, negative 4 divided by negative 2 is still negative 2. So notice, these two numbers are equal. It doesn't matter where we start and where we end. We just have to make sure that we have the directions right on how we're actually moving from one point to another.