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CCSS.Math:

find the slope of the line pictured on the graph so the slope of a line is defined to be rise over run or you could also view it as change in Y change in Y over change in x over change in X and let me show you what that means change in X so let's start at some arbitrary point on this line and they kind of they highlight some of these points so let's start it's one of these points right over here so if we wanted to start at one of these points and let's say we want to change our X in the positive direction so we want to go to the right so let's say we want to go from this point to this point over here how much do we have to move in X so if we want to move in X we have to go from this point to this point we're going from negative 3 to 0 so we're going from negative 3 to 0 so our change in X and this triangle that's Delta that means change in our change in X is equal to 3 so our change in X over here is equal to 3 so what was our change in Y when our change in X is equal to 3 well over that same when we moved from this point to this point our x value changed by 3 but what happened to our Y value what our Y value went down it went from positive 3 to positive 2 our Y value went down by 1 so our change in Y is equal to negative 1 so we rose negative 1 we actually went down so our rise is negative 1 when our run when our change in X is 3 so change in Y over change in X is negative 1 over 3 or we could say that our slope we could say that our slope is negative 1/3 let me scroll over a little bit it is negative 1/3 and I want to show you that we can do this but any two points on the line we could even go further than 3 in the X direction so let's let's go to the other way let's start at this point right over here and then move backwards to this point over here just to say that we'll still get the same result so to go from this point to that point what is change in X so our change in X is this right over here our change in X is that distance right over there we started at 3 and we went to negative 3 we went back 6 over here our change in X is equal to negative 6 we're starting at this point now so over here our change in X is negative 6 and then when our change in X is negative 6 when we start at this point and we move 6 back what is our change of y to get to that point well our y-value went from 1 that was our y-value at this point and then when we go back to this point our Y value is 3 so now our Y value is 3 so what did we do we moved up by 2 our change in Y is equal to 2 so over here our change in Y is equal to 2 slope is change in Y over change in X or rise over run change in Y is just rise change in X is just run how much you're moving in the horizontal direction so change in so rise over run in this example right over here is going to be there's going to be 2 over negative 6 which is the same thing as negative 1/3 and you could verify it for yourself take any of these 2 points start at one of these two points and figure out what is what is the run to get to the next point and then what is the rise to get at the next point and for any line the slope won't change let me do it again over here we had to move in the positive 3 direction so that is our run so this right here is positive 3 that's our run but what's our rise well we actually went down so we have a negative rise arises negative 1 so we have negative 1 is our rise we went down and our run was positive 3 so our slope here is negative 1/3