Worked example: average rate of change from table

what is the average rate of change of Y of X over the interval negative 5 is less than X is less than negative 2 so this is X is equal to negative 5 when X is equal to negative 5 y of X is equal to 6 and when X is equal to negative 2 y of X is equal to 0 so to figure out the average rate of change so the average rate of change of Y of X with respect and we can assume it's with respect to X with respect to X let me make that a little bit neater with respect to X this is going to be the change in Y of X over that interval over the change of X of that interval and the shorthand for change is this triangle symbol Delta Delta Y I'll just write Y I could write Delta Y of X its Delta Y change in Y over our change in X that's going to be our average rate of change over this interval so how much did Y change over this interval so Y went from a 6 to 0 so let's say that this is we can kind of view this as our end point right over here so this is our end this is our start and we could have done it the other way around we would get a consistent result but since this is higher up on the list let's call this the start and this is the X as a lower value we'll call that our start this is our end so we start at 6 we end at 0 so our change in Y is going to be negative 6 we went down by 6 in the Y direction it's negative 6 you could say that's 0 minus 6 and our change in X well we were at negative 5 and we go up to negative 2 we increased by 3 so we increased by 3 so we went when we increase X by 3 we went we decreased Y of X by 6 or if we want to simplify this right over here negative 6 over 3 is the same thing as negative 2 so our average rate of change of Y of X over the interval from negative 5 to negative 2 is negative 2 every time on bridge-ex increased 1y went down by negative 2