Question

Does the table show a proportional relationship? If so, what is the constant of proportionality (unit rate)?
hours $ earned
2 $ 15 3 $ 22.50 4 $ 30 5 $ 45

Answer 1

To determine if the table shows a proportional relationship, we need to check whether the ratio of $ earned to hours is constant for each pair.

Let's calculate the ratios for each pair:

1. For \(2\) hours:
\[
\text{Ratio} = \frac{15}{2} = 7.5
\]

2. For \(3\) hours:
\[
\text{Ratio} = \frac{22.50}{3} = 7.5
\]

3. For \(4\) hours:
\[
\text{Ratio} = \frac{30}{4} = 7.5
\]

4. For \(5\) hours:
\[
\text{Ratio} = \frac{45}{5} = 9
\]

Now, we can see that the ratios are:

- For \(2\) hours: \(7.5\)
- For \(3\) hours: \(7.5\)
- For \(4\) hours: \(7.5\)
- For \(5\) hours: \(9\)

The ratio becomes \(9\) for \(5\) hours, which does not match the other ratios. Therefore, the tables do not show a consistent proportional relationship.

As a result, there is no constant of proportionality for the given table.