Question

which table shows a proportional relationship between x and y?

option 1:

x	3	9	10	15
y	1	3	4	5

option 2:

x	1	5	8	10
y	15	75	120	150

option 3:

x	4	6	8	10
y	6	8	10	12

option 4:

x	2	3	5	6
y	3	4	7	9

Explanation:

Step1: Define proportional relationship

A proportional relationship between $x$ and $y$ means $\frac{y}{x} = k$ (constant) for all pairs, or $y=kx$.

Step2: Check first table

Calculate $\frac{y}{x}$ for each pair:
$\frac{1}{3} \approx 0.33$, $\frac{3}{9}=0.33$, $\frac{4}{10}=0.4$, $\frac{5}{15}\approx0.33$.
Not all ratios equal.

Step3: Check second table

Calculate $\frac{y}{x}$ for each pair:
$\frac{15}{1}=15$, $\frac{75}{5}=15$, $\frac{120}{8}=15$, $\frac{150}{10}=15$.
All ratios are equal (constant $k=15$).

Step4: Verify remaining tables (optional)

Third table: $\frac{6}{4}=1.5$, $\frac{8}{6}\approx1.33$ → not equal.
Fourth table: $\frac{3}{2}=1.5$, $\frac{4}{3}\approx1.33$ → not equal.

Answer:

The table with $x$ values 1, 5, 8, 10 and $y$ values 15, 75, 120, 150 (the second option) shows a proportional relationship.