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.

Question

Mathematics

Sophie

19 February, 23:23

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.

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Answers (2)

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Trinity Mayo · 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.

Summer Chapman · 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.