Question

Does the table show a proportional relationship? If so, what is the constant of proportionality (unit rate)?
Hours: 2, 3, 4, 5
Miles: 300, 350, 400, 700


Answers:
A. No, the table does not show a proportional relationship
B. Yes, the constant of proportionality is 100
C. Yes, the constant of proportionality is 150

Answer 1

To determine if the table shows a proportional relationship, we need to check if the ratio of miles to hours is constant for all pairs of values.

Let's calculate the ratio (miles per hour) for each pair:

1. For 2 hours:
\[
\text{Ratio} = \frac{300 \text{ miles}}{2 \text{ hours}} = 150 \text{ miles per hour}
\]

2. For 3 hours:
\[
\text{Ratio} = \frac{350 \text{ miles}}{3 \text{ hours}} \approx 116.67 \text{ miles per hour}
\]

3. For 4 hours:
\[
\text{Ratio} = \frac{400 \text{ miles}}{4 \text{ hours}} = 100 \text{ miles per hour}
\]

4. For 5 hours:
\[
\text{Ratio} = \frac{700 \text{ miles}}{5 \text{ hours}} = 140 \text{ miles per hour}
\]

Since these ratios (150, approximately 116.67, 100, and 140) are not the same, the table does not show a proportional relationship.

The correct answer is: **A. No, the table does not show a proportional relationship.**