Which table represents a proportional relationship?(1 point)

Question

Responses

x y
2 1
3 1.5
4 2
x y 2 1 3 1.5 4 2

x y
0 5
−1 5
−2 5
x y 0 5 negative 1 5 negative 2 5

x y
0 0
1 3
2 5
x y 0 0 1 3 2 5

x y
1 9
3 18
5 27 .

Answer 1

To determine which table represents a proportional relationship, we need to see if the ratio of \( y \) to \( x \) is constant for all pairs.

1. For the first table:

   • \( \frac{1}{2} = 0.5 \)
   • \( \frac{1.5}{3} = 0.5 \)
   • \( \frac{2}{4} = 0.5 \)
   • The ratio is constant 0.5. This is a proportional relationship.

2. For the second table:

   • \( \frac{5}{0} \) is undefined. All \( y \) values are the same for different \( x \) values. This is not a proportional relationship.

3. For the third table:

   • \( \frac{0}{0} \) is undefined (though the point (0,0) is included).
   • \( \frac{3}{1} = 3 \)
   • \( \frac{5}{2} = 2.5 \)
   • The ratios are not constant. This is not a proportional relationship.

4. For the fourth table:

   • \( \frac{9}{1} = 9 \)
   • \( \frac{18}{3} = 6 \)
   • \( \frac{27}{5} = 5.4 \)
   • The ratios are not constant. This is not a proportional relationship.

Based on the analysis, the first table is the only one that represents a proportional relationship.

Answer: The first table.