$\"\"$

Determine whether the given function is linear or non-linear.

First compute the average rate of change of $\"\"$ with respect to $\"\"$ and then compute the ratio of the consecutive outputs.

If the average rate of change is constant, then the function is linear else non-linear.

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\"\"

\"\"

Average rate of change

$\"\"$ $\"\"$

$\"\"$

$\"\"$ $\"\"$

$\"\"$

$\"\"$ $\"\"$

$\"\"$

$\"\"$ $\"\"$

$\"\"$

$\"\"$ $\"\"$

$\"\"$

Observe the table.

For the given function, the average rate of change is $\"\"$ .

Since the average rate of change is constant , the function is a linear function.

Definition of the slope :

If the average rate of change of the function is constant then slope of the line is the average rate of change of the function.

Slope of the linear function is $\"\"$ .

$\"\"$

The function is linear and the slope $\"\"$ .