To find the constant of proportionality (or unit rate) in the given table, we need to determine if there is a consistent ratio between the values of \( Y \) and \( X \).
Let's look at the pairs of values in the table:
- For \( X = 1 \), \( Y = 7 \)
- For \( X = 2 \), \( Y = 14 \)
- For \( X = 4 \), \( Y = 28 \)
- For \( X = 6 \), \( Y = 42 \)
To find the constant of proportionality \( k \), we can divide \( Y \) by \( X \) for any of the pairs:
- For \( X = 1 \) and \( Y = 7 \): \[ k = \frac{Y}{X} = \frac{7}{1} = 7 \]
- For \( X = 2 \) and \( Y = 14 \): \[ k = \frac{Y}{X} = \frac{14}{2} = 7 \]
- For \( X = 4 \) and \( Y = 28 \): \[ k = \frac{Y}{X} = \frac{28}{4} = 7 \]
- For \( X = 6 \) and \( Y = 42 \): \[ k = \frac{Y}{X} = \frac{42}{6} = 7 \]
In all cases, the constant of proportionality \( k \) is the same.
Therefore, the constant of proportionality (unit rate) is \( 7 \).