which table shows a proportional relationship between x and y?

Answer:

B.

Explanation:

Step1: Recall proportional - relationship formula

For a proportional relationship, $y = kx$, or $\frac{y}{x}=k$ (constant).

Step2: Check Table A

$\frac{-8.5}{-4.5}=\frac{17}{9}$, $\frac{-4}{3}\neq\frac{17}{9}$, not proportional.

Step3: Check Table B

$\frac{1.5}{-4.5}=-\frac{1}{3}$, $\frac{-1}{3}=-\frac{1}{3}$, $\frac{-2}{6}=-\frac{1}{3}$, $\frac{-3.5}{10.5}=-\frac{1}{3}$, proportional.

Step4: Check Table C

$\frac{-14}{-3}=\frac{14}{3}$, $\frac{-9.5}{-1.5}=\frac{19}{3}\neq\frac{14}{3}$, not proportional.

Step5: Check Table D

$\frac{-4}{-3}=\frac{4}{3}$, $\frac{-4.5}{-1.5}=3\neq\frac{4}{3}$, not proportional.