Which explains whether or not the values in the table represent a direct variation?

Question

x
4
6
10
20
y
1
1.5
2.5
5
The table represents a direct variation because the values are proportional.
The table represents a direct variation because the values are nonproportional.
The table does not represent a direct variation because the values are proportional.
The table does not represent a direct variation because the values are nonproportional.

Answer 1

To determine if the values in the table represent a direct variation, we need to check if the ratio \( \frac{y}{x} \) is constant for all pairs of \( (x, y) \).

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

1. For \( (4, 1) \): \[ \frac{1}{4} = 0.25 \]

2. For \( (6, 1.5) \): \[ \frac{1.5}{6} = 0.25 \]

3. For \( (10, 2.5) \): \[ \frac{2.5}{10} = 0.25 \]

4. For \( (20, 5) \): \[ \frac{5}{20} = 0.25 \]

Since the ratio \( \frac{y}{x} \) is the same (0.25) for all pairs of values, we can conclude that the values in the table represent a direct variation.

Therefore, the correct explanation is:

The table represents a direct variation because the values are proportional.