Question

gallons of gas 2 4 6 8 10
total cost 5.50, 11, 16.50, 22, 27.50
The constant of proportionality is
and the equation for this relationship is
.

Answer 1

what's the answer?

Answer 2

To find the constant of proportionality and the equation for the relationship between gallons of gas and total cost, we can analyze the data you've provided.

1. **Identify the constant of proportionality**:
The constant of proportionality \( k \) can be found by dividing the total cost by the gallons of gas. This should be the same for all values if the relationship is proportional.

\[
k = \frac{\text{Total Cost}}{\text{Gallons of Gas}}
\]

Let’s calculate \( k \) for the given points:

- For 2 gallons: \( k = \frac{5.50}{2} = 2.75 \)
- For 4 gallons: \( k = \frac{11}{4} = 2.75 \)
- For 6 gallons: \( k = \frac{16.50}{6} = 2.75 \)
- For 8 gallons: \( k = \frac{22}{8} = 2.75 \)
- For 10 gallons: \( k = \frac{27.50}{10} = 2.75 \)

The constant of proportionality \( k \) is **2.75**.

2. **Write the equation**:
Since the relationship is directly proportional, we can express it with the equation:

\[
\text{Total Cost} = k \times \text{Gallons of Gas}
\]

Substituting the value of \( k \):

\[
\text{Total Cost} = 2.75 \times \text{Gallons of Gas}
\]

So, the constant of proportionality is **2.75**, and the equation for this relationship is:

\[
\text{Total Cost} = 2.75 \times \text{Gallons of Gas}
\]