Which table represents a linear function?
Answer:
The table that represents a linear function is the one in which the values in the second column change at a constant rate.
In other words, the second column values increase or decrease by the same amount for every change in the first column values. To identify a linear function, we can look for a constant rate of change between the input (x) and output (y) values.
Let’s consider two tables as examples: Table A: x | y 1 | 3 2 | 5 3 | 7 4 | 9 Table B: x | y 1 | 2 3 | 4 5 | 6 7 | 8 In Table A, the difference between consecutive x-values is always 1, and the difference between consecutive y-values is always 2.
This means that for each increase of 1 in the x-values, there is an increase of 2 in the y-values. Hence, the rate of change is constant, indicating a linear function. In contrast, in Table B, the difference between consecutive x-values is always 2, but the difference between consecutive y-values is always 2 as well.
This means that for each increase of 2 in the x-values, there is an increase of 2 in the y-values. The rate of change is not constant, indicating a non-linear function. Therefore, Table A represents a linear function because it demonstrates a constant rate of change between the input and output values.
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