Question

HELP ASAP! Which of the following tables represents a linear function?

Table A -
x −2 −1 0 1 2
y 5 2 1 2 5

Table B -
x −2 −1 0 1 2
y 5 3 1 −1 −3

Table C -
x 3 3 0 3 3
y −2 −1 0 1 2

Table D -
x 0 1 2 3 4
y 0 −1 2 −3 4

Answer 1

Table B -

• x −2 −1 0 1 2
• y 5 3 1 −1 −3

Explanation:

You want to know which of the four offered tables represents a linear function.

Differences

A linear function will have differences in y that have the same ratio to differences in x for all pairs of values in the table.

Evaluation

Table A has x-differences that are 1 between adjacent terms. The y-differences are negative for the first pair of table values, but positive for the last pair (2 -5 vs 5 -2).

Table B has x-differences that are 1 between adjacent terms. The y-differences are -2 between any pair of adjacent terms, so their ratio to x-differences is -2/1 = -2, a constant. Table B represents a linear function.

Table C has x-differences that change from 0 to -3 to +3 while y-differences are constant at +1. The ratios of differences are not constant.

Table D has x-differences of +1, and y-differences that alternate in sign and magnitude.

Only Table B represents a linear function.

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