Does the table show a proportional relationship? If so, what is the constant of proportionality (unit rate)?

Question

hours miles
2 300 3 350 4 400 5 700

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 each pair of values.

Let's calculate the ratios:

1. For 2 hours and 300 miles: \[ \frac{300}{2} = 150 \]

2. For 3 hours and 350 miles: \[ \frac{350}{3} \approx 116.67 \]

3. For 4 hours and 400 miles: \[ \frac{400}{4} = 100 \]

4. For 5 hours and 700 miles: \[ \frac{700}{5} = 140 \]

Now we compare the calculated ratios:

• For 2 hours: 150
• For 3 hours: approximately 116.67
• For 4 hours: 100
• For 5 hours: 140

Since the ratios are not the same, the table does not show a proportional relationship. There is no constant of proportionality (unit rate) for this data set.