Which of these tables represents a linear function?
A: 3,3
4,4
5,6
6,7
B: 3,6***
4,5
5,4
6,3
C: 3,7
4,6
5,5
6,5
D: 3,2
4,4
5,5
6,6
The table that represents a linear function is table B: 3,6; 4,5; 5,4; 6,3. This is because the x-values (3, 4, 5, 6) increase by 1 each time, and the y-values (6, 5, 4, 3) decrease by 1 each time, showing a constant rate of change.
To check which table represents a linear function, you need to see if there is a constant rate of change between the x-values and the corresponding y-values. In a linear function, the rate of change or slope will remain the same throughout the table.
Let's analyze each table:
A: The second x-value is always one more than the first x-value, and the second y-value is always one more than the first y-value. The rate of change is constant at 1. Therefore, Table A represents a linear function.
B: The x-values increase by 1 each time, but the y-values decrease by 1. The rate of change is not constant, so Table B does not represent a linear function.
C: The x-values increase by 1 each time, but the y-values decrease by 1 and then stay the same. The rate of change is not constant, so Table C does not represent a linear function.
D: The x-values increase by 1 each time, and the y-values increase by more than 1. The rate of change is not constant, so Table D does not represent a linear function.
Therefore, the correct answer is Table A.