Question

Which table of values represents a linear function?
A
xx yy
22 minus, 5−5
33 minus, 1−1
44 33
55 66
B
xx yy
33 minus, 3−3
55 00
77 33
99 66
C
xx yy
22 minus, 6−6
55 minus, 1−1
77 44
99 99
D
xx yy
minus, 6−6 88
minus, 2−2 55
33 22
88 minus, 1−1
Answer

Answer 1

To determine which table of values represents a linear function, we need to check if the change in the y-values is consistent for equal changes in the x-values (constant rate of change or slope).

### Table A
- (2, -5) to (3, -1): Change in y = -1 - (-5) = 4; Change in x = 3 - 2 = 1
- (3, -1) to (4, 3): Change in y = 3 - (-1) = 4; Change in x = 4 - 3 = 1
- (4, 3) to (5, 6): Change in y = 6 - 3 = 3; Change in x = 5 - 4 = 1

**Not linear** (different changes in y).

### Table B
- (3, -3) to (5, 0): Change in y = 0 - (-3) = 3; Change in x = 5 - 3 = 2
- (5, 0) to (7, 3): Change in y = 3 - 0 = 3; Change in x = 7 - 5 = 2
- (7, 3) to (9, 6): Change in y = 6 - 3 = 3; Change in x = 9 - 7 = 2

**Linear** (constant change in y for constant change in x).

### Table C
- (2, -6) to (5, -1): Change in y = -1 - (-6) = 5; Change in x = 5 - 2 = 3
- (5, -1) to (7, 4): Change in y = 4 - (-1) = 5; Change in x = 7 - 5 = 2
- (7, 4) to (9, 9): Change in y = 9 - 4 = 5; Change in x = 9 - 7 = 2

**Not linear** (different changes in x with the same change in y).

### Table D
- (-6, 8) to (-2, 5): Change in y = 5 - 8 = -3; Change in x = -2 - (-6) = 4
- (-2, 5) to (3, 2): Change in y = 2 - 5 = -3; Change in x = 3 - (-2) = 5
- (3, 2) to (8, -1): Change in y = -1 - 2 = -3; Change in x = 8 - 3 = 5

**Not linear** (different changes in x with the same change in y).

### Conclusion
Only **Table B** represents a linear function.