Linear & nonlinear functions: table

does the following table represent a linear equation so let's see what's going on here when X is negative 7 y is 4 then when X is negative 3 y is 3 so let's see what happened toward what our change in X was so our change in X and I could even write it over here our change in X so going from negative 7 to negative 3 we had an increase in 4 and X and what was our change in Y and this triangle that's just the Greek letter Delta it's shorthand for change in well our change in Y when X increased by 4 we went our Y value went from 4 to 3 so our change in Y is negative 1 now in order for this to be a linear equation the ratio between our change in Y and our change in X has to be constant so our change in Y over change in X for any two points on in this equation or any two points at the table has to be the same constant when when exchanged by for Y changed by negative 1 or when Y changed by negative 1 X changed by 4 so it has to be we have to have a constant change in Y with respect to X of negative 1/4 let's see if this is true so the next two points when I go from negative 3 to 1 once again I'm increasing X by 4 and once again I'm decreasing Y by negative 1 so we have that same ratio now so let's look at this last point when we go from 1 to 7 in the x-direction we are increasing by 6 and when we go from 2 to 1 we are still decreasing by 1 so now this ratio for the slot going to this last from this third point to this fourth point is negative 1 over 6 so it is not so 4 just for this last point right over here for this last point our change in Y over change in X or I should say really between these last two points right over here our change in Y over change in X let me clear this up our change in let me make it clear so just between these last and magenta just between these last two points over here our change in Y is negative 1 and our change in X is 6 so we have a different rate of change of Y with respect X because we had a different rate of change of Y with respect to X or ratio between our change in Y and change in X this is not a linear equation no not a linear equation