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

Answer:

- Constant.

- Linear

Step-by-step 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:

$rate\ of\ change=\frac{change\ in\ y}{change\ in\ x}$

It can be also written as:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's substitute into  $m=\frac{y_2-y_1}{x_2-x_1}$ the following points:

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

$m=\frac{22-11}{2-1}\\\\m=11$

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

$m=\frac{33-22}{3-2}\\\\m=11$

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

$m=\frac{44-33}{4-3}\\\\m=11$

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.