Answer:
Please check the explanation.
Step-by-step explanation:
The slope-intercept form of the linear function
[tex]y = mx+b[/tex]
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
