Question

Which table shows a proportional relationship between x and y?

A.
x y
2 9
4 18
6 27
8 36
10 45
B.
x y
2 2
4 8
6 18
8 32
10 50
C.
x y
1 4
2 7
3 10
4 13
5 16
D.
x y
1 5
2 6
3 7
4 8
5 9

Answer 1

To determine which table shows a proportional relationship between \( x \) and \( y \), we need to look for a constant ratio \( \frac{y}{x} \) for all values of \( x \) and \( y \).

Let's examine each table:

**A.**
- \( \frac{9}{2} = 4.5 \)
- \( \frac{18}{4} = 4.5 \)
- \( \frac{27}{6} = 4.5 \)
- \( \frac{36}{8} = 4.5 \)
- \( \frac{45}{10} = 4.5 \)

All ratios are equal \( (4.5) \), so this table represents a proportional relationship.

**B.**
- \( \frac{2}{2} = 1 \)
- \( \frac{8}{4} = 2 \)
- \( \frac{18}{6} = 3 \)
- \( \frac{32}{8} = 4 \)
- \( \frac{50}{10} = 5 \)

The ratios are not constant, so this table does not represent a proportional relationship.

**C.**
- \( \frac{4}{1} = 4 \)
- \( \frac{7}{2} = 3.5 \)
- \( \frac{10}{3} \approx 3.33 \)
- \( \frac{13}{4} = 3.25 \)
- \( \frac{16}{5} = 3.2 \)

The ratios are not constant, so this table does not represent a proportional relationship.

**D.**
- \( \frac{5}{1} = 5 \)
- \( \frac{6}{2} = 3 \)
- \( \frac{7}{3} \approx 2.33 \)
- \( \frac{8}{4} = 2 \)
- \( \frac{9}{5} = 1.8 \)

The ratios are not constant, so this table does not represent a proportional relationship.

The only table that shows a proportional relationship is:

**Table A.**