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