Either Table A or Table B shows a proportional relationship. Table A

x −2 −1 0 1
y 2 3 0 5

Table B

x −1 0 1 2
y −3 0 3 6

Plot the points from the table that shows a proportional relationship.

Table B shows a proportional relationship

Explanation:

In a proportional relationship two quantities vary directly with each other.

So,

y ∝ x

y = kx

Where, k is the constant of variation.

The ordered pairs of table A are (-2,2), (-1,3), (0,0) and (1,5).

From these ordered pairs we can conclude that the value of y-coordinate is not changing according to the x-coordinate because the values of x increased by 1 for each ordered pair but the value of y is not increasing in the same proportion..

The ordered pairs of table B are (-1,-3), (0,0), (1,3) and (2,6). The value of y increasing at a constant rate 3 and the value of y-coordinate is 3 times of x-coordinate.

Choose any two ordered pairs of table B. Let the two points are (0,0) and (1,3).

The proportional relationship is defined as

y = 3x

Therefore, 3 is the constant of variation and rate of change.

So, Table B shows a proportional relationship.

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