Which Table Represents A Linear Function?

The table below explains the bird speed ƒ (χ ) over times in seconds, χ. Which of these two tables represents a linear relationship?

To know whether a table describes a linear relationship, check the rate of change in the entire table.

In the first table, the value of y doesn't increase or decrease from a constant amount in each increase of unit 1 in the value of x. It increases by 4, then reaches 8, then 16, and further.

In the second table, the value of y increases constantly by 6 with each increase of unit 1 in the value of x.

So, here, the first table shows a non-linear function, whereas the second table shows a linear function. In any case, the greater the change rate, the more the value of y changes for every increase in the value of x.

Now, when the point on the graph creates a straight line which is not vertical, its function counts as a linear function. When there is a table in place of the graph, you must always see the rate of change. If it is in the input to change in the output is the similar for each point in the table. So, the table shows a linear function.

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