Does the table show a proportional relationship? How do you know?

Question

X Y
2 8
3 14
4 16
6 22

(1 point)
Responses

No, because the numbers are all even.
No, because the numbers are all even.

No, because the unit rate is not constant.
No, because the unit rate is not constant.

Yes, because the unit rate is the same in each row.
Yes, because the unit rate is the same in each row.

Yes, because the numbers are all even.

Answer 1

To determine if the table shows a proportional relationship, we need to check if the unit rate (the ratio of \(Y\) to \(X\)) is constant for all pairs of \(X\) and \(Y\).

Let's calculate the ratios of \(Y\) to \(X\) for each pair:

• For \(X = 2\), \(Y = 8\): \[ \text{Ratio} = \frac{Y}{X} = \frac{8}{2} = 4 \]

• For \(X = 3\), \(Y = 14\): \[ \text{Ratio} = \frac{Y}{X} = \frac{14}{3} \approx 4.67 \]

• For \(X = 4\), \(Y = 16\): \[ \text{Ratio} = \frac{Y}{X} = \frac{16}{4} = 4 \]

• For \(X = 6\), \(Y = 22\): \[ \text{Ratio} = \frac{Y}{X} = \frac{22}{6} \approx 3.67 \]

The calculated ratios are:

• \(4\) (for \(X = 2\))
• \(4.67\) (for \(X = 3\))
• \(4\) (for \(X = 4\))
• \(3.67\) (for \(X = 6\))

Since the ratios are not constant across all pairs, we conclude that there is no proportional relationship.

Thus, the correct response is: No, because the unit rate is not constant.