Question

Find the constant of proportionality (unit rate) in the table.
X Y
1 7
2 14
4 28
6 42

(1 point)
Responses

(1, 7)
(1, 7)

(2, 14)
(2, 14)

(4, 28)
(4, 28)

(6, 42)

Answer 1

To find the constant of proportionality (unit rate) in the given table, we can examine the relationship between the values of \(X\) and \(Y\).

The relationship appears to have the form \(Y = kX\), where \(k\) is the constant of proportionality.

Let's calculate \(k\) for each pair of values:

For \(X = 1\):
\[
Y = 7 \Rightarrow k = \frac{Y}{X} = \frac{7}{1} = 7
\]

For \(X = 2\):
\[
Y = 14 \Rightarrow k = \frac{Y}{X} = \frac{14}{2} = 7
\]

For \(X = 4\):
\[
Y = 28 \Rightarrow k = \frac{Y}{X} = \frac{28}{4} = 7
\]

For \(X = 6\):
\[
Y = 42 \Rightarrow k = \frac{Y}{X} = \frac{42}{6} = 7
\]

In each case, the constant of proportionality \(k\) is 7. Thus, the unit rate is 7.

So the correct answer is:

**7**