Question

A taxi service charges $1.25 every mile you travel.
Could the relationship between the cost in dollars and the distance in miles be proportional?
Number of miles (m) Cost in dollars (c) Cost per mile (
m
c
​
)
5 $6.25 1.25
8 $10.00 1.25
20 $25.00 1.25

The relationship could be proportional.

The relationship could not be proportional

Answer 1

To determine if the relationship between the cost in dollars and the distance in miles is proportional, we need to check if the cost per mile is constant across different distances.

In this case, the taxi service charges $1.25 every mile traveled. Let's look at the cost (c) for each distance (m) you provided:

1. For 5 miles:
\[
c = 1.25 \times 5 = 6.25 \ \text{dollars}
\]
Cost per mile: \( \frac{c}{m} = \frac{6.25}{5} = 1.25 \)

2. For 8 miles:
\[
c = 1.25 \times 8 = 10.00 \ \text{dollars}
\]
Cost per mile: \( \frac{c}{m} = \frac{10.00}{8} = 1.25 \)

3. For 20 miles:
\[
c = 1.25 \times 20 = 25.00 \ \text{dollars}
\]
Cost per mile: \( \frac{c}{m} = \frac{25.00}{20} = 1.25 \)

In all cases, the cost per mile is constant at $1.25. Since the ratio \( \frac{c}{m} \) remains the same regardless of the distance traveled, the relationship between the cost in dollars and the distance in miles is indeed proportional.

Thus, we can conclude:

**The relationship could be proportional.**