Question

Which table could represent a proportional relationship?
A.
x 1 2 5 11
y 1,300 2,600 6,500 14,300
B.
x 1 2 5 11
y 1,150 2,250 4,500 12,300
C.
x 1 2 5 11
y 900 1,800 3,500 7,640

Answer 1

To determine which table represents a proportional relationship, we need to check if \( \frac{y}{x} \) remains constant for each pair of \( (x, y) \) values in the tables.

Let's calculate \( \frac{y}{x} \) for each option:

**Option A:**
- For \( x = 1, y = 1,300 \): \( \frac{y}{x} = \frac{1,300}{1} = 1,300 \)
- For \( x = 2, y = 2,600 \): \( \frac{y}{x} = \frac{2,600}{2} = 1,300 \)
- For \( x = 5, y = 6,500 \): \( \frac{y}{x} = \frac{6,500}{5} = 1,300 \)
- For \( x = 11, y = 14,300 \): \( \frac{y}{x} = \frac{14,300}{11} \approx 1,300 \)

All values yield 1,300, so **Option A** represents a proportional relationship.

**Option B:**
- For \( x = 1, y = 1,150 \): \( \frac{y}{x} = \frac{1,150}{1} = 1,150 \)
- For \( x = 2, y = 2,250 \): \( \frac{y}{x} = \frac{2,250}{2} = 1,125 \)
- For \( x = 5, y = 4,500 \): \( \frac{y}{x} = \frac{4,500}{5} = 900 \)
- For \( x = 11, y = 12,300 \): \( \frac{y}{x} = \frac{12,300}{11} \approx 1,118.18 \)

The values are not constant, so **Option B** does not represent a proportional relationship.

**Option C:**
- For \( x = 1, y = 900 \): \( \frac{y}{x} = \frac{900}{1} = 900 \)
- For \( x = 2, y = 1,800 \): \( \frac{y}{x} = \frac{1,800}{2} = 900 \)
- For \( x = 5, y = 3,500 \): \( \frac{y}{x} = \frac{3,500}{5} = 700 \)
- For \( x = 11, y = 7,640 \): \( \frac{y}{x} = \frac{7,640}{11} \approx 694.55 \)

The values are not constant, so **Option C** does not represent a proportional relationship.

Thus, the only table that represents a proportional relationship is **Option A**.