Question

Nicholas and his friends set out to sea on their annual fishing trip.
This table shows the relationship between the time (in hours) Nicholas and his friends spend sailing, x, and their distance from shore (in miles), y.
x (hours) y (miles)
1 14
2 28
3 42
5 70
According to the values in the table, do x and y have a proportional relationship?
yes
no
What is the constant of proportionality? Write your answer as a whole number or decimal.
miles per hour

Answer 1

To determine if \(x\) (time in hours) and \(y\) (distance in miles) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for the provided values.

Let’s calculate the ratio for each pair of values from the table:

1. For \(x = 1\), \(y = 14\):
\[
\frac{y}{x} = \frac{14}{1} = 14
\]

2. For \(x = 2\), \(y = 28\):
\[
\frac{y}{x} = \frac{28}{2} = 14
\]

3. For \(x = 3\), \(y = 42\):
\[
\frac{y}{x} = \frac{42}{3} = 14
\]

4. For \(x = 5\), \(y = 70\):
\[
\frac{y}{x} = \frac{70}{5} = 14
\]

Since the ratio \(\frac{y}{x} = 14\) is constant for all pairs, then \(x\) and \(y\) do have a proportional relationship.

Therefore, **yes**, \(x\) and \(y\) have a proportional relationship.

The constant of proportionality is **14 miles per hour**.