Question

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

x	0	2	4	6
y	0	5	10	15

b)

x	0	1	2	3
y	0	1.5	3	4.5

c)

x	0	\\(\frac{1}{5}\\)	\\(\frac{2}{5}\\)	\\(\frac{3}{5}\\)
y	0	\\(\frac{1}{2}\\)	1	\\(1\frac{1}{2}\\)

d)

x	0	\\(\frac{1}{2}\\)	\\(\frac{1}{3}\\)	\\(\frac{1}{4}\\)
y	0	\\(\frac{1}{4}\\)	\\(\frac{1}{9}\\)	\\(\frac{1}{16}\\)

Explanation:

Step1: Define proportional relationship

A proportional relationship follows $y = kx$, so $\frac{y}{x}$ is constant for all non-zero $x$.

Step2: Check Table A

Calculate $\frac{y}{x}$ for non-zero $x$:
$\frac{5}{2}=2.5$, $\frac{10}{4}=2.5$, $\frac{15}{6}=2.5$
Constant ratio, so proportional.

Step3: Check Table B

Calculate $\frac{y}{x}$ for non-zero $x$:
$\frac{1.5}{1}=1.5$, $\frac{3}{2}=1.5$, $\frac{4.5}{3}=1.5$
Constant ratio, so proportional.

Step4: Check Table C

Calculate $\frac{y}{x}$ for non-zero $x$:
$\frac{\frac{1}{2}}{\frac{1}{5}}=\frac{5}{2}=2.5$, $\frac{1}{\frac{2}{5}}=\frac{5}{2}=2.5$, $\frac{1\frac{1}{2}}{\frac{3}{5}}=\frac{\frac{3}{2}}{\frac{3}{5}}=\frac{5}{2}=2.5$
Constant ratio, so proportional.

Step5: Check Table D

Calculate $\frac{y}{x}$ for non-zero $x$:
$\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}$, $\frac{\frac{1}{9}}{\frac{1}{3}}=\frac{1}{3}$, $\frac{\frac{1}{16}}{\frac{1}{4}}=\frac{1}{4}$
Ratio is not constant, so not proportional.

Answer:

A.)
B.)
C.)