Tell whether each function is linear or non-linear. Function A Function B x 0 1 2 3 y 0 1 8 27 y = –x + 5

Please check the explanation.

Step-by-step explanation:

The slope-intercept form of the linear function  

where

The graph of y = mx + b is a straight line. Thus, y = mx + b represents a linear function.

Analzing the function y = –x + 5

Given the linear function

y = –x + 5

comparing with the slope-intercept form of linear equation

The slope m = -1

The y-intercept b = 5

Also, the graph of a linear function is a straight line.

Thus,

The function  y = –x + 5 represents  a linear function.

Analzing the Table Function

x        0     1     2     3

y        0     1     8     27

In order to identify whether the given table represents the linear function or not, we need to make sure the given function has a constant change x and y.

If there is a constant change in x and y, then it would be a linear Function otherwise it would not represent a linear function.

There is a constant change in x values.

i.e.

1 - 0 = 1

2 - 1 = 1

3 - 2 = 1

But, there is NOT a constant change in y.

i.e.

1 - 0 = 0

8 - 1 = 7

27 - 8 = 19

It is clear that the table does not have a constant change in y-values.

Therefore, the table function does not represent the linear function