Which table of values represents a linear function?

Question

A
xx yy
minus, 3−3 99
minus, 1−1 88
44 55
66 44
B
xx yy
minus, 1−1 minus, 1−1
22 11
55 33
88 55
C
xx yy
minus, 8−8 00
minus, 2−2 33
33 66
88 99
D
xx yy
22 minus, 8−8
44 minus, 2−2
66 33
88 88
Answer
Multiple Choice Answers
AA
BB
CC
DD

Answer 1

To determine which table of values represents a linear function, we need to see if the changes in \( y \) correspond consistently with the changes in \( x \). In a linear function, the ratio of change (slope) between \( y \) and \( x \) should remain constant.

Let's analyze each table:

Table A

| x | y | |----|----| | -3 | 9 | | -1 | 8 | | 4 | 5 | | 6 | 4 |

Calculating changes:

• From \(-3\) to \(-1\): \( y \) changes from \( 9 \) to \( 8 \) (change of -1)
• From \(-1\) to \( 4\): \( y \) changes from \( 8 \) to \( 5 \) (change of -3)
• From \( 4 \) to \( 6 \): \( y \) changes from \( 5 \) to \( 4 \) (change of -1)

The changes in \( y \) are inconsistent (not constant).

Table B

| x | y | |----|----| | -1 | -1 | | 2 | 1 | | 5 | 3 | | 8 | 5 |

Calculating changes:

• From \(-1\) to \( 2\): \( y \) changes from \( -1 \) to \( 1 \) (change of +2)
• From \( 2\) to \( 5\): \( y \) changes from \( 1 \) to \( 3 \) (change of +2)
• From \( 5\) to \( 8\): \( y \) changes from \( 3 \) to \( 5 \) (change of +2)

The changes in \( y \) are consistent (all changes equal +2).

Table C

| x | y | |-----|----| | -8 | 0 | | -2 | 3 | | 3 | 6 | | 8 | 9 |

Calculating changes:

• From \(-8\) to \(-2\): \( y \) changes from \( 0 \) to \( 3 \) (change of +3)
• From \(-2\) to \( 3\): \( y \) changes from \( 3 \) to \( 6 \) (change of +3)
• From \( 3\) to \( 8\): \( y \) changes from \( 6 \) to \( 9 \) (change of +3)

The changes in \( y \) are consistent (all changes equal +3).

Table D

| x | y | |----|----| | 2 | -8 | | 4 | -2 | | 6 | 3 | | 8 | 8 |

Calculating changes:

• From \( 2\) to \( 4\): \( y \) changes from \( -8 \) to \( -2 \) (change of +6)
• From \( 4\) to \( 6\): \( y \) changes from \( -2 \) to \( 3 \) (change of +5)
• From \( 6\) to \( 8\): \( y \) changes from \( 3 \) to \( 8 \) (change of +5)

The changes in \( y \) are inconsistent (not constant).

Conclusion

• Table A: Not linear
• Table B: Linear
• Table C: Linear
• Table D: Not linear

Both Table B and Table C represent linear functions, but since the question typically expects a single answer, let's select Table B given that it has a simpler and more explicit pattern.

The answer is B.