What is slope and how is it calculated

And one thing I want to do, I want to show you that I could have really picked any two points here. Let's say I didn't pick-- let me clear this out-- let's say I didn't pick those two points, let me pick some other points, and I'll even go in a different direction. I want to show you that you're going to get the same answer. Let's say I've used this as my starting point, and I want to go all the way over there.

Well, let's think about the change in y first. So the change in y, I'm going down by how many units? I went from 1 to negative 3, that's negative 4. That's my change in y.

Change in y is equal to negative 4. Now what is my change in x? Well I'm going from this point, or from this x value, all the way-- let me do that in a different color-- all the way back like this.

So I'm going to the left, so it's going to be a negative change in x, and I went 1, 2, 3, 4, 5, 6 units back. So my change in x is equal to negative 6. And you can even see I started it at x is equal to 3, and I went all the way to x is equal to negative 3.

That's a change of negative 6. I went 6 to the left, or a change of negative 6. So what is my change in y over change in x? My change in y over change in x is equal to negative 4 over negative 6. The negatives cancel out and what's 4 over 6? Well, that's just 2 over 3. So it's the same value, you just have to be consistent.

If this is my start point, I went down 4, and then I went back 6. Negative 4 over negative 6. If I viewed this as my starting point, I could say that I went up 4, so it would be a change in y would be 4, and then my change in x would be 6.

The run can be calculated as 8. Thus, the slope is Determine the velocity i. When you believe you know the answer and not before , click the button to check it. The velocity i. Instead you must pick two points as discussed in this part of the lesson and divide the change in y by the change in x.

Physics Tutorial. My Cart Subscription Selection. Student Extras. Time Graphs. The illustration shows how the terrain slope at a given elevation grid cell can be calculated from elevations of the eight grid cells that surround it. First, north-south slope is calculated from the grid columns. Then east-west slope is calculated from the grid rows. The square root of the sum of the north-south slope and east-west slope, multiplied by , equals the percent slope at the original grid cell.

The fancy technical term for the procedure is "neighborhood algorithm. The neighborhood algorithm calculates slope for every cell in an elevation grid by analyzing each 3 x 3 neighborhood. Percent slope can be converted to slope degree later.

The result is a grid of slope values suitable for use in various soil loss and hydrologic models. Slope Slope is a measure of change in elevation. A rise of feet over a run of feet yields a percent slope.