Welcome to another video from UltimatAlgebra.com. In this video, we will learn how to find the slope from a graph.

 

We learnt earlier that the slope is the change in y, over the change in x. The change in y simply means how many points you are going up or down. If you are going up, then you have a positive change. If you are going down, then you have a negative change.

The change in x simply means how many points you are going to the right or left. If you are going to the right, then you have a positive change. If you are going to the left, then you have a negative change.

Take a moment and let this sink in. It is the basis of most of the things we will be doing with slopes and graphs.

 

Let’s find the slope of this graph.

Our first step will be to choose any two points on the line. I am choosing these two points. Let me call them A and B.

You can choose any two points on the line. However, it is important to choose points that will make your work easier. Choose points whose x and y values can be easily determined. Normally points at the corners are best. Any of these points would have worked well also.

 

Now to find the slope all we are doing is moving from one point of the line to the other on the slope triangle.

Let’s move from B to A. We moved down 2 points. Notice moving down is negative. So, we have negative 2 here. Then we will move to the left 1 to get to A. Notice again that moving to the left is negative. We have negative 1 here. negative 2 over negative 1 is simply 2.

So our slope is 2.

 

We could have also moved from A to B. Let’s look at it. We have our slope triangle here. We move 2 points up. Moving up is positive, so, we have 2. Then we will move to the right 1. Moving to the right is positive. So we have 1.

2 over 1 is simply 2. We notice that we got the same answer.

 

There are other things you can do, but I don’t want to get you confused with that. Notice that our first movement is always change in y. That is moving up or down, then our second movement is change in x. That is moving left or right

 

 

If you can tell the type of slope easily, then you can choose not to bother with the negative or positive movement.

From this graph, we can say the change in y is 2. The change in x is 1. We know that our graph has a positive slope so our answer is simply positive 2.

 

Let’s look at this graph to make this idea clearer. We can see that our change in y is 3. Our change in x is 2. We know that this is a negative slope. So, we have negative 3 over 2.

 

 

This brings us to this very important topic. Please master it because we will be using the idea repeatedly. Have a great day. Good bye