The data cannot be modeled by a linear equation because the rate of change is not constant. This can be seen in the fact that when you increase x from 1 to 2, you subtract 3 from the y-values. However, as you add 2 more, you continue to subtract 3 from the y-values. If the function were a linear function, we would likely subtract 6 from the y-values, since that would form a constant ratio.
You can even look at the fact that as we increased the x by 4, we continued to decrease the y by 3. This does not form a constant ratio, and is thus the data could not be modeled by a linear function.