Question

Is the function represented by the table linear? x y 10 –6 11 1 12 6 13 12 Yes, because it has a constant rate of change. Yes, because it does not have a constant rate of change. No, because it has a constant rate of change. No, because it does not have a constant rate of change.

Answer 1

The rate of change may be calculated through the equation,

(yn - y(n-1))/ (xn - x(n-1))

For the first pair, (10, -6) and (11,1)
r1 = (1 --6)/(11 - 10)
r1 = 7

For the second pair, (12, 6) and (13, 12)
r2 = (12 - 6)/(13-12)
r2 = 6

Since the values of 2r's are not the same, the equation is not linear.

The answer is the last choice.

Answer 2

For this case, you can graph the given table and observe that it is not a linear function.
The reason in this case would be the following:
No, because it does not have a constant rate of change.
Note: However, it should be noted that it has a very good approximation to a linear function.