Answer:
Table B shows a proportional relationship.
Step-by-step explanation:
In a proportional relationship two quantities vary directly with each other. It means
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
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), then the constant of variation is
[tex]k=\frac{y_2-y_1}{x_2-x_1}=\frac{3-0}{1-0}=3[/tex]
The proportional relationship is defined as
[tex]y=3x[/tex]
Therefore, 3 is the constant of variation and rate of change.
So, Table B shows a proportional relationship.
