Question

select all tables that represent a proportional relationship between x and y.
a.)

x	0	3	6	9
y	0	6	12	18

b.)

x	0	2	4	6
y	0	4	16	36

c.)

x	0	4	8	12
y	0	5	9	13

d.)

x	0	1	2	3
y	0	3	6	9

Explanation:

Step1: Check proportionality for Table A

Calculate $\frac{y}{x}$ for non-zero $x$:
$\frac{6}{3}=2$, $\frac{12}{6}=2$, $\frac{18}{9}=2$

Step2: Check proportionality for Table B

Calculate $\frac{y}{x}$ for non-zero $x$:
$\frac{4}{2}=2$, $\frac{16}{4}=4$, $\frac{36}{6}=6$

Step3: Check proportionality for Table C

Calculate $\frac{y}{x}$ for non-zero $x$:
$\frac{5}{4}=1.25$, $\frac{9}{8}=1.125$, $\frac{13}{12}\approx1.083$

Step4: Check proportionality for Table D

Calculate $\frac{y}{x}$ for non-zero $x$:
$\frac{3}{1}=3$, $\frac{6}{2}=3$, $\frac{9}{3}=3$

Answer:

A.) The table with x: 0, 3, 6, 9; y: 0, 6, 12, 18
D.) The table with x: 0, 1, 2, 3; y: 0, 3, 6, 9