Question

The rate of change for the interval shown in the table is (constant/non constant), so the function is a (linear/non-linear) function.

Answer 1

- Constant.

- Linear

Explanation:

Te Rate of change of a line is also known as "Slope" and it is constant.

It is important to remember that, by definition, this is given by:

`rate\ of\ change=(change\ in\ y)/(change\ in\ x)`

It can be also written as:

`m=(y_2-y_1)/(x_2-x_1)`

Let's substitute into
`m=(y_2-y_1)/(x_2-x_1)` the following points:

1) Points (1,11) and (2,22)

`m=(22-11)/(2-1)\\\\m=11`

2) Points (2,22) and (3,33):

`m=(33-22)/(3-2)\\\\m=11`

3) Points (3,33) and (4,44):

`m=(44-33)/(4-3)\\\\m=11`

As you can notice, the rate of change (or the slope) of the function given in the table, is always constant.

Therefore you can conclude that it is a Linear Function.