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

Answer 1

To determine if \( x \) (time in hours) and \( y \) (distance in miles) have a proportional relationship, we can check if the ratio of \( y \) to \( x \) is constant for all pairs of values.

Let's compute the ratios:

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

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

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

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

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

Therefore, the answer is **yes**.