Since the cost of deli meat is proportional to its weight, we can express this relationship with the equation:
\[ C = k \cdot w \]
where:
- \( C \) is the cost,
- \( w \) is the weight in pounds, and
- \( k \) is the constant of proportionality (cost per pound).
From the information given, Nigel paid $10 for 2.12 pounds of roast beef. We can find the value of \( k \) by substituting these values into the equation:
\[ 10 = k \cdot 2.12 \]
To find \( k \), we divide both sides by 2.12:
\[ k = \frac{10}{2.12} \approx 4.72 \]
So the equation representing the proportional relationship is:
\[ C = 4.72w \]
This means the cost \( C \) in dollars is equal to approximately $4.72 times the weight \( w \) in pounds.